tabita57i

2021-02-09

Given:
$A=\left[\left[-2,3\right],\left[0,1\right]\right]$
$B=\left[\left[8,1\right],\left[5,4\right]\right]$
Find the following matrices:
a. A + B
b. A - B
c. -4A
d. 3A + 2B.

Brittany Patton

a) A+B
$A+B=\left[\left[-2,3\right],\left[0,1\right]\right]+\left[\left[8,1\right],\left[5,4\right]\right]$
$=\left[\left[-2+8,3+1\right],\left[0+5,1+4\right]\right]$
$=\left[\left[6,4\right],\left[5,5\right]\right]$
b) A-B
$A-B=\left[\left[-2,3\right],\left[0,1\right]\right]-\left[\left[8,1\right],\left[5,4\right]\right]$
$=\left[\left[-2-8,3-1\right],\left[0-5,1-4\right]\right]$
$=\left[\left[-10,2\right],\left[-5,-3\right]\right]$
c) -4A
$-4A=-4\left[\left[-2,3\right],\left[0,1\right]\right]$
$=\left[\left[-4\ast -2,-4\ast 3\right],\left[-4\ast 0,-4\ast 1\right]\right]$
$=\left[\left[8,-12\right],\left[0,-4\right]\right]$
d)3A+2B
$3A+2B=3\left[\left[-2,3\right],\left[0,1\right]\right]+2\left[\left[8,1\right],\left[5,4\right]\right]$
$=\left[\left[-6,9\right],\left[0,3\right]\right]+\left[\left[16,2\right],\left[10,8\right]\right]$
$=\left[\left[-6+16,9+2\right],\left[0+10,3+8\right]\right]$
$=\left[\left[10,11\right],\left[10,11\right]\right]$

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