Question

Find the following matrices: a) A + B.(b) A - B.(c) -4A.(d) 3A + 2B.

Matrices
ANSWERED
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)\(3A+2B=\begin{bmatrix}26 & 2 & -3 \end{bmatrix}\)

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