Find the following matrices: a) A+B. (b) A−B. (c) -4A. (d) 3A+2B. A=[62−3],B=[4−23]

Step 1 Given matrices:A=[62−3],B=[4−23] To find: a) A+B. (b) A−B. (c) -4A. (d) 3A+2B. Solution: A=[62−3],B=[4−23] a)A+B=[62−3]+[4−23] ⇒A+B=[(6+4)(2−2)(−3+3)] ⇒A+B=[1000] b) A−B=[62−3]−[4−23] ⇒A−B=[(6−4)(2−(−2))(−3−3)] ⇒A−B=[24−6] c)−4A=−4[62−3] ⇒−4A=[−24−812] d)3A+2B=3[62−3]+2[4−23] ⇒3A+2B=[186−9]+[8−46] ⇒3A+2B=[(18+8)(6−4)(−9+6)] ⇒3A+2B=[262−3] Step 2 Result a)A+B=[1000] b)A−B=[24−6] c)−4A=[−24−812] d)3A+2B=[262−3]

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2021-02-02

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

Answer & Explanation

Caren

Skilled2021-02-03Added 96 answers

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

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