Question

Find the following matrices:a) A + B.(b) A - B.(c) -4A.A=begin{bmatrix}2 & -10&-2 14 & 12&104&-2&2 end{bmatrix} , B=begin{bmatrix}6 & 10&-2 0 & -12&-4-5&2&-2 end{bmatrix}

Matrices
ANSWERED
asked 2021-03-07

Find the following matrices:
a) \(A + B\).
(b) \(A - B\).
(c) \(-4A\).
\(A=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix} , B=\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)

Answers (1)

2021-03-08
Given,
\(A=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix} , B=\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)
a)\(A+B=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix}+\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)
\(=\begin{bmatrix}2+6 & -10+10&-2-2 \\14+0 & 12-12&10-4\\4-5&-2+2&2-2 \end{bmatrix}\)
\(=\begin{bmatrix}8 & 0&-4 \\14 & 0&6\\-1&0&0 \end{bmatrix}\)
Step 2
b)\(A-B=\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix}-\begin{bmatrix}6 & 10&-2 \\0 & -12&-4\\-5&2&-2 \end{bmatrix}\)
\(=\begin{bmatrix}2-6 & -10-10&-2-(-2) \\14-0 & 12-(-12)&10-(-4)\\4-(-5)&-2-2&2-(-2) \end{bmatrix}\)
\(=\begin{bmatrix}-4 & -20&0 \\14 & 24&14\\9&-4&4 \end{bmatrix}\)
c)\(-4A=-4\begin{bmatrix}2 & -10&-2 \\14 & 12&10\\4&-2&2 \end{bmatrix}\)
\(=\begin{bmatrix}-4(2) & -4(-10)&-4(-2) \\-4(14) & -4(12)&-4(10)\\-4(4)&-4(-2)&-4(2) \end{bmatrix}\)
\(=\begin{bmatrix}-8 & 40&8 \\-56 & -48&-40\\-16&8&-8 \end{bmatrix}\)
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