Let matrix X = \begin{bmatrix} 5 & -3 \\ 2 & 1 \end{bmatrix} and matrix Y = \begin{bmatrix… — ACT

Let matrix $X = \begin{bmatrix} 5 & -3 \\ 2 & 1 \end{bmatrix}$ and matrix $Y = \begin{bmatrix} 1 & 4 \\ -2 & 3 \end{bmatrix}$ . If $Z = X - Y$ , what is the value of the element in the first row and second column of $Z$ ?

Answer: -7

Answer

The correct answer is

-7

To find the element in the first row and second column of matrix

Z = X - Y

, we subtract the element in the first row and second column of matrix

Y

from the corresponding element in matrix

X

. The element in the first row and second column of

X

-3

, and the element in the first row and second column of

Y

4

. Subtracting these values gives

-3 - 4 = -7

Step-by-Step Solution

Identify the elements in the first row and second column for both matrices.

x_{1,2} = -3

and

y_{1,2} = 4

To find the element in the first row and second column of the resulting matrix

Z

, we must use the corresponding elements from matrices

X

and

Y

Subtract the element of

Y

from the element of

X

-3 - 4 = -7

Since

Z = X - Y

, each element

z_{i,j}

of the resulting matrix is calculated as

x_{i,j} - y_{i,j}

Key Concept

Matrix Subtraction

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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