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Common Core: High School - Algebra : Matrix Representation of Linear Equations: CCSS.Math.Content.HSA-REI.C.8

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Example Questions

Example Question #1 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations 44 x - 5 y + 33 z = -1 , 40 x + 18 y - 28 z = -8 , 18 x - 18 y + 3 z = -17 into proper matrix form.

Possible Answers:

$\begin{bmatrix} 44 & -5 & 33 \\ 40 & -28 & 18 \\ 18 & -1 & -18 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ -17 \end{bmatrix}$

$\begin{bmatrix} 44 & -5 & 33 \\ 40 & 18 & -28 \\ 18 & -18 & -1 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ -17 \end{bmatrix}$

$\begin{bmatrix} 44 & 40 & 18 \\ -5 & 18 & -18 \\ 33 & -28 & -1 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ -17 \end{bmatrix}$

$\begin{bmatrix} -5 & 44 & 33 \\ 18 & 40 & -28 \\ -1 & -18 & 18 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ -17 \end{bmatrix}$

$\begin{bmatrix} 44 & -5 & 33 \\ 40 & 18 & -28 \\ 18 & -18 & -1 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ -17 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 44 & -5 & 33 \\ 40 & 18 & -28 \\ 18 & -18 & -1 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ -17 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} 44 & -5 & 33 \\ 40 & 18 & -28 \\ 18 & -18 & -1 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -1 \\ -8 \\ 33 \end{bmatrix}$

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Example Question #2 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 29 x - 30 y + 36 z = -37 , - 14 x + 48 y + 35 z = -37 , - 23 x + 19 y + z = -1 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -29 & -30 & 36 \\ -14 & 35 & 48 \\ -23 & -43 & 19 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ -1 \end{bmatrix}$

$\begin{bmatrix} -29 & -30 & 36 \\ -14 & 48 & 35 \\ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ -1 \end{bmatrix}$

$\begin{bmatrix} -29 & -14 & -23 \\ -30 & 48 & 19 \\ 36 & 35 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ -1 \end{bmatrix}$

$\begin{bmatrix} -30 & -29 & 36 \\ 48 & -14 & 35 \\ -43 & 19 & -23 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ -1 \end{bmatrix}$

$\begin{bmatrix} -29 & -30 & 36 \\ -14 & 48 & 35 \\ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ -1 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -29 & -30 & 36 \\ -14 & 48 & 35 \\ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ -1 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -29 & -30 & 36 \\ -14 & 48 & 35 \\ -23 & 19 & -43 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -37 \\ -37 \\ 36 \end{bmatrix}$

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Example Question #3 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 5 x + 12 y + 35 z = 0 , 3 x - 13 y - 6 z = 9 , 48 x + 15 y + 2 z = -19 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -5 & 3 & 48 \\ 12 & -13 & 15 \\ 35 & -6 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ -19 \end{bmatrix}$

$\begin{bmatrix} 12 & -5 & 35 \\ -13 & 3 & -6 \\ 44 & 15 & 48 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ -19 \end{bmatrix}$

$\begin{bmatrix} -5 & 12 & 35 \\ 3 & -13 & -6 \\ 48 & 15 & 44 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ -19 \end{bmatrix}$

$\begin{bmatrix} -5 & 12 & 35 \\ 3 & -13 & -6 \\ 48 & 15 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ -19 \end{bmatrix}$

$\begin{bmatrix} -5 & 12 & 35 \\ 3 & -6 & -13 \\ 48 & 44 & 15 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ -19 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -5 & 12 & 35 \\ 3 & -13 & -6 \\ 48 & 15 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ -19 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -5 & 12 & 35 \\ 3 & -13 & -6 \\ 48 & 15 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 0 \\ 9 \\ 35 \end{bmatrix}$

Report an Error

Example Question #4 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 37 x - 43 y + 33 z = 13 , 34 x - 29 y + 2 z = -6 , - 14 x + 27 y + 4 z = 35 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -37 & -43 & 33 \\ 34 & -29 & 2 \\ -14 & 27 & 35 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 35 \end{bmatrix}$

$\begin{bmatrix} -37 & 34 & -14 \\ -43 & -29 & 27 \\ 33 & 2 & 35 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 35 \end{bmatrix}$

$\begin{bmatrix} -37 & -43 & 33 \\ 34 & -29 & 2 \\ -14 & 27 & 35 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 35 \end{bmatrix}$

$\begin{bmatrix} -43 & -37 & 33 \\ -29 & 34 & 2 \\ 35 & 27 & -14 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 35 \end{bmatrix}$

$\begin{bmatrix} -37 & -43 & 33 \\ 34 & 2 & -29 \\ -14 & 35 & 27 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 35 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -37 & -43 & 33 \\ 34 & -29 & 2 \\ -14 & 27 & 35 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 35 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -37 & -43 & 33 \\ 34 & -29 & 2 \\ -14 & 27 & 35 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 13 \\ -6 \\ 33 \end{bmatrix}$

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Example Question #5 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 34 x + 29 y - 19 z = 40 , - 48 x + 9 y - 13 z = 30 , - 47 x + 37 y + 5 z = 23 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -34 & -48 & -47 \\ 29 & 9 & 37 \\ -19 & -13 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ 23 \end{bmatrix}$

$\begin{bmatrix} -34 & 29 & -19 \\ -48 & 9 & -13 \\ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ 23 \end{bmatrix}$

$\begin{bmatrix} -34 & 29 & -19 \\ -48 & -13 & 9 \\ -47 & -3 & 37 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ 23 \end{bmatrix}$

$\begin{bmatrix} 29 & -34 & -19 \\ 9 & -48 & -13 \\ -3 & 37 & -47 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ 23 \end{bmatrix}$

$\begin{bmatrix} -34 & 29 & -19 \\ -48 & 9 & -13 \\ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ 23 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -34 & 29 & -19 \\ -48 & 9 & -13 \\ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ 23 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -34 & 29 & -19 \\ -48 & 9 & -13 \\ -47 & 37 & -3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 40 \\ 30 \\ -19 \end{bmatrix}$

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Example Question #6 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 47 x + 3 y + 37 z = 2 , 18 x + 37 y - 27 z = 42 , 31 x - 20 y + 6 z = -28 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -47 & 3 & 37 \\ 18 & 37 & -27 \\ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ -28 \end{bmatrix}$

$\begin{bmatrix} -47 & 3 & 37 \\ 18 & -27 & 37 \\ 31 & 29 & -20 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ -28 \end{bmatrix}$

$\begin{bmatrix} -47 & 18 & 31 \\ 3 & 37 & -20 \\ 37 & -27 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ -28 \end{bmatrix}$

$\begin{bmatrix} 3 & -47 & 37 \\ 37 & 18 & -27 \\ 29 & -20 & 31 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ -28 \end{bmatrix}$

$\begin{bmatrix} -47 & 3 & 37 \\ 18 & 37 & -27 \\ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ -28 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -47 & 3 & 37 \\ 18 & 37 & -27 \\ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ -28 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -47 & 3 & 37 \\ 18 & 37 & -27 \\ 31 & -20 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ 42 \\ 37 \end{bmatrix}$

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Example Question #7 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 46 x + 10 y + 19 z = -3 , - 11 x - 16 y + 49 z = -31 , 13 x - 35 y + 7 z = -2 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -46 & 10 & 19 \\ -11 & -16 & 49 \\ 13 & -35 & -46 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ -2 \end{bmatrix}$

$\begin{bmatrix} -46 & 10 & 19 \\ -11 & 49 & -16 \\ 13 & -46 & -35 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ -2 \end{bmatrix}$

$\begin{bmatrix} 10 & -46 & 19 \\ -16 & -11 & 49 \\ -46 & -35 & 13 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ -2 \end{bmatrix}$

$\begin{bmatrix} -46 & -11 & 13 \\ 10 & -16 & -35 \\ 19 & 49 & -46 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ -2 \end{bmatrix}$

$\begin{bmatrix} -46 & 10 & 19 \\ -11 & -16 & 49 \\ 13 & -35 & -46 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ -2 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -46 & 10 & 19 \\ -11 & -16 & 49 \\ 13 & -35 & -46 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ -2 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -46 & 10 & 19 \\ -11 & -16 & 49 \\ 13 & -35 & -46 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} -3 \\ -31 \\ 19 \end{bmatrix}$

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Example Question #8 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations 39 x + 34 y - 35 z = 2 , 16 x + 7 y + 31 z = -44 , - 48 x + 29 y + 8 z = 37 into proper matrix form.

Possible Answers:

$\begin{bmatrix} 39 & 34 & -35 \\ 16 & 7 & 31 \\ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ 37 \end{bmatrix}$

$\begin{bmatrix} 34 & 39 & -35 \\ 7 & 16 & 31 \\ 44 & 29 & -48 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ 37 \end{bmatrix}$

$\begin{bmatrix} 39 & 34 & -35 \\ 16 & 7 & 31 \\ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ 37 \end{bmatrix}$

$\begin{bmatrix} 39 & 34 & -35 \\ 16 & 31 & 7 \\ -48 & 44 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ 37 \end{bmatrix}$

$\begin{bmatrix} 39 & 16 & -48 \\ 34 & 7 & 29 \\ -35 & 31 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ 37 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 39 & 34 & -35 \\ 16 & 7 & 31 \\ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ 37 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} 39 & 34 & -35 \\ 16 & 7 & 31 \\ -48 & 29 & 44 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 2 \\ -44 \\ -35 \end{bmatrix}$

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Example Question #9 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Put the equations - 31 x - 26 y - 48 z = 19 , 4 x + 42 y - 12 z = 35 , 36 x + 29 y + 9 z = 10 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & 4 & 36 \\ -26 & 42 & 29 \\ -48 & -12 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ -48 \end{bmatrix}$

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Example Question #131 : Reasoning With Equations & Inequalities

Put the equations - 31 x - 26 y - 48 z = 19 , 4 x + 42 y - 12 z = 35 , 36 x + 29 y + 9 z = 10 into proper matrix form.

Possible Answers:

$\begin{bmatrix} -26 & -31 & -48 \\ 42 & 4 & -12 \\ 49 & 29 & 36 \end{bmatrix} \cdot \begin{bmatrix} x \\ z \\ y \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & -12 & 42 \\ 36 & 49 & 29 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} y \\ z \\ x \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

$\begin{bmatrix} -31 & 4 & 36 \\ -26 & 42 & 29 \\ -48 & -12 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ 10 \end{bmatrix}$

Explanation:

In order to put these equations into proper matrix form, let's look at the general form.

$\begin{bmatrix} x_1 & y_1 & z_1 \\ x_2 & y_2 & z_2 \\ x_3 & y_3 & z_3 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} a \\ b \\ c\end{bmatrix}$

The variables in the first matrix correspond to the coefficients in the equations and the variables in the third matrix correspond to the answers of the equations.

Now, let's substitute for each variable in the matrices.

$\begin{bmatrix} -31 & -26 & -48 \\ 4 & 42 & -12 \\ 36 & 29 & 49 \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ z \end{bmatrix}=\begin{bmatrix} 19 \\ 35 \\ -48 \end{bmatrix}$

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Common Core: High School - Algebra : Matrix Representation of Linear Equations: CCSS.Math.Content.HSA-REI.C.8

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #1 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #2 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #3 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #4 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #5 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #6 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #7 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #8 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #9 : Matrix Representation Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.8

Example Question #131 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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