Questions: Question 23 B = [[-5, 8], [0, -3], [2, 7]]. Calculate 4B+A. [[-11, 25], [3, -7], [8, 34]] [[31, -20], [12, 17], [2, 31]] [[16, 4], [12, 8], [8, 52]] [[-11, 25], [3, 2], [2, 13]]

Transcript text: Question 23 $B=\left[\begin{array}{cc} -5 & 8 \\ 0 & -3 \\ 2 & 7 \end{array}\right]$. Calculate $4 B+A$. $\left[\begin{array}{cc}-11 & 25 \\ 3 & -7 \\ 8 & 34\end{array}\right]$ $\left[\begin{array}{cc}31 & -20 \\ 12 & 17 \\ 2 & 31\end{array}\right]$ $\left[\begin{array}{cc}16 & 4 \\ 12 & 8 \\ 8 & 52\end{array}\right]$ $\left[\begin{array}{cc}-11 & 25 \\ 3 & 2 \\ 2 & 13\end{array}\right]$

Solution

Solution Steps

Step 1: Define Matrix $ B $

Given the matrix $ B $: \[ B = \begin{bmatrix} -5 & 8 \\ 0 & -3 \\ 2 & 7 \end{bmatrix} \]

Step 2: Define Matrix $ A $

Assuming matrix $ A $ is a zero matrix of the same size as $ B $: \[ A = \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{bmatrix} \]

Step 3: Calculate $ 4B + A $

To find $ 4B + A $, we first calculate $ 4B $: \[ 4B = 4 \cdot \begin{bmatrix} -5 & 8 \\ 0 & -3 \\ 2 & 7 \end{bmatrix} = \begin{bmatrix} 4 \cdot -5 & 4 \cdot 8 \\ 4 \cdot 0 & 4 \cdot -3 \\ 4 \cdot 2 & 4 \cdot 7 \end{bmatrix} = \begin{bmatrix} -20 & 32 \\ 0 & -12 \\ 8 & 28 \end{bmatrix} \]

Now, we add $ A $ to $ 4B $: \[ 4B + A = \begin{bmatrix} -20 & 32 \\ 0 & -12 \\ 8 & 28 \end{bmatrix} + \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{bmatrix} = \begin{bmatrix} -20 & 32 \\ 0 & -12 \\ 8 & 28 \end{bmatrix} \]

Step 4: Present the Final Result

The result of the operation $ 4B + A $ is: \[ 4B + A = \begin{bmatrix} -20 & 32 \\ 0 & -12 \\ 8 & 28 \end{bmatrix} \]