Questions: Given the matrices A and B shown below, find 1/4 B - A. A = [[5, -2, 6], [-3, -1, 4]] B = [[20, 24, -16], [-44, -44, 20]]

Given the matrices A and B shown below, find 1/4 B - A. A = [[5, -2, 6], [-3, -1, 4]] B = [[20, 24, -16], [-44, -44, 20]]
Transcript text: Given the matrices $A$ and $B$ shown below, find $\frac{1}{4} B-A$. \[ A=\left[\begin{array}{ccc} 5 & -2 & 6 \\ -3 & -1 & 4 \end{array}\right] \quad B=\left[\begin{array}{ccc} 20 & 24 & -16 \\ -44 & -44 & 20 \end{array}\right] \]
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Solution

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Solution Steps

Step 1: Calculate (1/4)B

Multiply each element of matrix B by (1/4):

(1/4)B = [(1/4)_20 (1/4)_24 (1/4)_-16] [(1/4)_-44 (1/4)_-44 (1/4)_20 ]

(1/4)B = [5 6 -4] [-11 -11 5]

Step 2: Calculate (1/4)B - A

Subtract matrix A from (1/4)B:

(1/4)B - A = [5-5 6-(-2) -4-6] [-11-(-3) -11-(-1) 5-4]

(1/4)B - A = [0 8 -10] [-8 -10 1]

Final Answer

[0 8 -10] [-8 -10 1]

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