Common Core: High School - Algebra : Use Matrix Inverse to Solve System of Linear Equations: CCSS.Math.Content.HSA-REI.C.9

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

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Example Questions

Example Question #1 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 84 & -21 \\ 0 & 0 \end{bmatrix}

Possible Answers:

Yes

No

Correct answer:

No

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , , , and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 84 \cdot 0 - -21 \cdot 0

\displaystyle \det(A)= 0 - 0

\displaystyle \det(A)= 0

Example Question #2 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 33 & -28 \\ -21 & 84 \end{bmatrix}

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 33 \cdot -21 - -28 \cdot 84

\displaystyle \det(A)= -693 - -2352

\displaystyle \det(A)= 1659

Example Question #1 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 55 & -83 \\ 45 & -51 \end{bmatrix}

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 55 \cdot 45 - -83 \cdot -51

\displaystyle \det(A)= 2475 - 4233

\displaystyle \det(A)= -1758

Example Question #4 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 85 & -90 \\ 96 & -67 \end{bmatrix}

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 85 \cdot 96 - -90 \cdot -67

\displaystyle \det(A)= 8160 - 6030

\displaystyle \det(A)= 2130

Example Question #1 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 81 & -66 \\ -43 & 13 \end{bmatrix}

Possible Answers:

No

Yes

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 81 \cdot -43 - -66 \cdot 13

\displaystyle \det(A)= -3483 - -858

\displaystyle \det(A)= -2625

Example Question #2 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} -75 & 50 \\ 85 & -50 \end{bmatrix}

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= -75 \cdot 85 - 50 \cdot -50

\displaystyle \det(A)= -6375 - -2500

\displaystyle \det(A)= -3875

Example Question #3 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 88 & 96 \\ 59 & -92 \end{bmatrix}

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 88 \cdot 59 - 96 \cdot -92

\displaystyle \det(A)= 5192 - -8832

\displaystyle \det(A)= 14024

Example Question #4 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} 46 & -46 \\ 68 & -68 \end{bmatrix}

Possible Answers:

No

Yes

Correct answer:

No

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where , and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= 46 \cdot 68 - -46 \cdot -68

\displaystyle \det(A)= 3128 - 3128

\displaystyle \det(A)= 0

Example Question #5 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} -59 & 43 \\ 36 & -89 \end{bmatrix}

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= -59 \cdot 36 - 43 \cdot -89

\displaystyle \det(A)= -2124 - -3827

\displaystyle \det(A)= 1703

Example Question #6 : Use Matrix Inverse To Solve System Of Linear Equations: Ccss.Math.Content.Hsa Rei.C.9

Does the following matrix have an inverse?

\displaystyle A=\begin{bmatrix} -64 & -60 \\ -69 & 21 \end{bmatrix}

Possible Answers:

Yes

No

Correct answer:

Yes

Explanation:

In order to determine if a matrix has an inverse is to calculate the determinant.

Where  and  correspond to the entries in the following matrix.

\displaystyle \begin{bmatrix} a & b \\ c & d \end{bmatrix}

If the determinant is not equal to zero, an inverse exists, and if it's equal to zero, no inverse exists.

Now let's calculate the determinant.

\displaystyle \det(A)= -64 \cdot -69 - -60 \cdot 21

\displaystyle \det(A)= 4416 - -1260

\displaystyle \det(A)= 5676

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