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GRE Subject Test: Math : Matrix Operations

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Matrix Operations

Perform the following operation.

$\begin{bmatrix} 2& 4& 1\\ 5& 3& -2\\ -3& -1&0 \end{bmatrix}$ $\cdot \begin{bmatrix} 2\\ 4\\ 1 \end{bmatrix}$ $+\begin{bmatrix} -7\\ 4\\ 11 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 14& 24& 1 \end{bmatrix}$

$\begin{bmatrix} 7\\ 20\\ 7 \end{bmatrix}$

$\begin{bmatrix} 34\\ -25\\ 7 \end{bmatrix}$

$\begin{bmatrix} 14\\ 24 \\ 1 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 14\\ 24 \\ 1 \end{bmatrix}$

Explanation:

The first step to solving this operation is to do the multiplication:

$\begin{bmatrix} 2& 4& 1\\ 5& 3& -2\\ -3& -1&0 \end{bmatrix}$ $\cdot \begin{bmatrix} 2\\ 4\\ 1 \end{bmatrix}$ $=\begin{bmatrix} 2(2)& 4(4)& 1(1)\\ 5(2)& 3(4)& -2(1)\\ -3(2)& -1(4)&0(1) \end{bmatrix}$ $=\begin{bmatrix} 4+16+1\\ 10+12-2\\ -6-4+0 \end{bmatrix}$ $=\begin{bmatrix} 21\\ 20\\ -10 \end{bmatrix}$

Once we have multiplied the matrices, we can perform the addition portion:

$\begin{bmatrix} 21\\ 20\\ -10 \end{bmatrix} + \begin{bmatrix} -7\\ 4\\ 11 \end{bmatrix} = \begin{bmatrix} 14\\ 24\\ 1 \end{bmatrix}$

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Example Question #2 : Matrix Operations

Perform the following operation.

$3\left(\begin{bmatrix} 7\\ -3\\ 2 \end{bmatrix}+\begin{bmatrix} -1\\ 4\\ 6 \end{bmatrix}\right)$

Possible Answers:

$\begin{bmatrix} 4\\ 9\\ 20 \end{bmatrix}$

$\begin{bmatrix} 18& 3& 24 \end{bmatrix}$

$\begin{bmatrix} 20\\ -5\\ 12 \end{bmatrix}$

$\begin{bmatrix} 18\\ 3\\ 24 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 18\\ 3\\ 24 \end{bmatrix}$

Explanation:

The first step is to solve whatever is in the parentheses, in this case it is addition:

$\begin{bmatrix} 7\\ -3\\ 2 \end{bmatrix}+\begin{bmatrix} -1\\ 4\\ 6 \end{bmatrix}=\begin{bmatrix} 6\\ 1\\ 8 \end{bmatrix}$

We then substitute our solution into the parentheses:

$3\left(\begin{bmatrix} 6\\ 1\\ 8 \end{bmatrix}\right)$

Our next, and final step in this problem, is to carry out the multiplication:

$3\left(\begin{bmatrix} 6\\ 1\\ 8 \end{bmatrix}\right)=\begin{bmatrix} 18\\ 3\\ 24 \end{bmatrix}$

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GRE Subject Test: Math : Matrix Operations

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Matrix Operations

Example Question #2 : Matrix Operations

All GRE Subject Test: Math Resources

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