Question

If \[ A = \begin{bmatrix} 3 & 6 \\ -5 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 7 & 8 \\ 5 & 6 \end{bmatrix}, \] then \[ 6A - 5B = \] The correct answer is:

• A. \( \begin{bmatrix} 17 & 5 \\ 4 & 54 \end{bmatrix} \)
• B. \( \begin{bmatrix} 17 & 5 \\ -4 & 54 \end{bmatrix} \)
• C. \( \begin{bmatrix} -17 & -55 \\ -4 & -6 \end{bmatrix} \)
• D. \( \begin{bmatrix} 17 & -55 \\ -4 & -54 \end{bmatrix} \)

Hint:

When performing matrix operations like addition or subtraction, ensure that the matrices have the same dimensions. Perform operations element-wise.

Answer 1

The Correct Option is C

First, calculate \( 6A \): \[ 6A = 6 \begin{bmatrix} 3 & 6 \\ -5 & 4 \end{bmatrix} = \begin{bmatrix} 18 & 36 \\ -30 & 24 \end{bmatrix}. \]

Next, calculate \( 5B \): \[ 5B = 5 \begin{bmatrix} 7 & 8 \\ 5 & 6 \end{bmatrix} = \begin{bmatrix} 35 & 40 \\ 25 & 30 \end{bmatrix}. \]

Now subtract \( 5B \) from \( 6A \): \[ 6A - 5B = \begin{bmatrix} 18 & 36 \\ -30 & 24 \end{bmatrix} - \begin{bmatrix} 35 & 40 \\ 25 & 30 \end{bmatrix}. \]

Simplify by subtracting corresponding elements: \[ 6A - 5B = \begin{bmatrix} 18 - 35 & 36 - 40 \\ -30 - 25 & 24 - 30 \end{bmatrix} = \begin{bmatrix} -17 & -4 \\ -55 & -6 \end{bmatrix}. \]

Therefore, the result is: \[ \boxed{ 6A - 5B = \begin{bmatrix} -17 & -4 \\ -55 & -6 \end{bmatrix}. } \]

Correct Answer:

(C) \( \begin{bmatrix} -17 & -4 \\ -55 & -6 \end{bmatrix} \)