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

Let matrix $A = \begin{bmatrix} 3 & -2 \\ 5 & 1 \end{bmatrix}$ and matrix $B = \begin{bmatrix} -2 & 3 \\ 2 & -3 \end{bmatrix}$ . If matrix $C$ is defined by the equation $C = 3A - 2B$ , what is the value of the element in the second row and first column of $C$ ?

Answer: 11

Answer

The element in the second row and first column of matrix

C

is 11.

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

C

, we apply the operations defined by

C = 3A - 2B

directly to the corresponding elements of

A

and

B

. The element in row 2, column 1 of matrix

A

5

, and of matrix

B

2

. Computing

3(5) - 2(2)

yields

15 - 4 = 11

Step-by-Step Solution

Identify the elements in the second row and first column of matrices

A

and

B

A_{21} = 5

and

B_{21} = 2

To find a specific element of the resulting matrix

C = 3A - 2B

, we only need to perform the operations on the elements in the corresponding position.

Set up the equation for the element in the second row and first column of

C

C_{21} = 3A_{21} - 2B_{21}

Matrix addition, subtraction, and scalar multiplication are performed element-wise.

Substitute the identified values into the equation and compute the result.

C_{21} = 3(5) - 2(2) = 15 - 4 = 11

Evaluating the expression gives the value of the target element.

Key Concept

Matrix scalar multiplication and element-wise subtraction

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic