Find the following matrices: a) A + B. (b) A - B. (c) -4A. (d) 3A + 2B. A=begin{bmatrix}6 & 2 & -3 end{bmatrix} , B=begin{bmatrix}4 & -2 & 3 end{bmatrix}

Find the following matrices: a) A + B. (b) A - B. (c) -4A. (d) 3A + 2B. A=begin{bmatrix}6 & 2 & -3 end{bmatrix} , B=begin{bmatrix}4 & -2 & 3 end{bmatrix}

Question
Matrices
asked 2021-02-02
Find the following matrices: a) A + B.
(b) A - B.
(c) -4A.
(d) 3A + 2B.
\(A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)

Answers (1)

2021-02-03
Step 1
Given matrices:\(A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)
To find:
a) A + B.
(b) A - B.
(c) -4A.
(d) 3A + 2B.
Solution:
\(A=\begin{bmatrix}6 & 2 & -3 \end{bmatrix} , B=\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)
a)\(A+B=\begin{bmatrix}6 & 2 & -3 \end{bmatrix}+\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)
\(\Rightarrow A+B=\begin{bmatrix}(6+4) & (2-2) & (-3+3) \end{bmatrix}\)
\(\Rightarrow A+B=\begin{bmatrix}10 & 0 & 0 \end{bmatrix}\)
b) \(A-B=\begin{bmatrix}6 & 2 & -3 \end{bmatrix}-\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)
\(\Rightarrow A-B=\begin{bmatrix}(6-4) & (2-(-2)) & (-3-3) \end{bmatrix}\)
\(\Rightarrow A-B=\begin{bmatrix}2 & 4 & -6 \end{bmatrix}\)
c)\(-4A=-4\begin{bmatrix}6 & 2 & -3 \end{bmatrix}\)
\(\Rightarrow -4A=\begin{bmatrix}-24 & -8 & 12 \end{bmatrix}\)
d)\(3A+2B=3\begin{bmatrix}6 & 2 & -3 \end{bmatrix}+2\begin{bmatrix}4 & -2 & 3 \end{bmatrix}\)
\(\Rightarrow 3A+2B=\begin{bmatrix}18 & 6 & -9 \end{bmatrix}+\begin{bmatrix}8 & -4 & 6 \end{bmatrix}\)
\(\Rightarrow 3A+2B=\begin{bmatrix}(18+8) & (6-4) & (-9+6) \end{bmatrix}\)
\(\Rightarrow 3A+2B=\begin{bmatrix}26 & 2 & -3 \end{bmatrix}\)
Step 2
Result
a)\(A+B=\begin{bmatrix}10 & 0 & 0 \end{bmatrix}\)
b)\(A-B=\begin{bmatrix}2 & 4 & -6 \end{bmatrix}\)
c)\(-4A=\begin{bmatrix}-24 & -8 & 12 \end{bmatrix}\)
d)\(3A+2B=\begin{bmatrix}26 & 2 & -3 \end{bmatrix}\)
0

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