Find the matrices: a)A + B b) A - B c) -4A d)3A + 2B A=begin{bmatrix}4 & 1 3 & 2 end{bmatrix} ,B=begin{bmatrix}5 & 9 0 & 7 end{bmatrix}

Find the matrices: a)A + B b) A - B c) -4A d)3A + 2B A=begin{bmatrix}4 & 1 3 & 2 end{bmatrix} ,B=begin{bmatrix}5 & 9 0 & 7 end{bmatrix}

Question
Matrices
asked 2021-01-31
Find the matrices:
a)A + B
b) A - B
c) -4A
d)3A + 2B
\(A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}\)

Answers (1)

2021-02-01
Step 1: Given:
We have matrices \(A=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} ,B=\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}\)
We have to answer the following.
Step 2: Calculation
a) A+B
\(\Rightarrow A+B=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix}+\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}=\begin{bmatrix}9 & 10 \\ 3 & 9 \end{bmatrix}\)
b) A-B
\(\Rightarrow A-B=\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix}-\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}=\begin{bmatrix} -1 & -8 \\ 3 & -5 \end{bmatrix}\)
c) -4A
\(\Rightarrow -4A=-4 \begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix} = \begin{bmatrix} -16 & -4 \\ -12 & -8 \end{bmatrix}\)
d) 3A+2B
\(\Rightarrow 3A+2B=3\begin{bmatrix}4 & 1 \\ 3 & 2 \end{bmatrix}+2\begin{bmatrix}5 & 9 \\ 0 & 7 \end{bmatrix}=\begin{bmatrix} 12 & 3 \\ 9 & 6 \end{bmatrix} + \begin{bmatrix} 10 & 18 \\ 0 & 14 \end{bmatrix} = \begin{bmatrix} 22 & 21 \\ 9 & 20 \end{bmatrix}\)
0

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