If 3A - 2B - 1 -2- 3 0 - and 2A - 3B - -3 3- 1 -1 - then find B

3A 2B =[ #160; #160; 1 #160; amp; 2 #160;; #160; #160; 3 #160; amp; 0 #160; ] 2A 3B =[ #160; #160; 3 #160; #160; amp; 3 ...

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Byju's Answer

Standard XII

Mathematics

Addition and Subtraction of a Matrix

If 3A - 2B ...

Question

If $3 A - 2 B = (\begin{matrix} 1 & - 2 3 & 0 \end{matrix})$ and $2 A - 3 B = (\begin{matrix} - 3 & 3 1 & - 1 \end{matrix})$ then find $B$

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Solution

$3 A - 2 B = (\begin{matrix} 1 & - 2 3 & 0 \end{matrix})$

$2 A - 3 B = (\begin{matrix} - 3 & 3 1 & - 1 \end{matrix})$

$2 (3 A - 2 B) - 3 (2 A - 3 B)$ $= 6 A - 4 B - 6 A + 9 B$

$5 B = 2 (\begin{matrix} 1 & - 2 3 & 0 \end{matrix}) - 3 (\begin{matrix} - 3 & 3 1 & - 1 \end{matrix})$

$5 B = (\begin{matrix} 2 & - 4 6 & 0 \end{matrix}) - (\begin{matrix} - 9 & 9 3 & - 3 \end{matrix})$

$5 B = (\begin{matrix} 2 - 9 & - 4 - 9 6 - 3 & 0 + 3 \end{matrix})$

$5 B = (\begin{matrix} - 7 & - 13 3 & 3 \end{matrix})$

$B = \frac{1}{5} (\begin{matrix} - 7 & - 13 3 & 3 \end{matrix})$

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If 3A−2B=(1−230) and 2A−3B=(−331−1) then find B

3A−2B=(1−230)2A−3B=(−331−1)2(3A−2B)−3(2A−3B)=6A−4B−6A+9B5B=2(1−230)−3(−331−1)5B=(2−460)−(−993−3)5B=(2−9−4−96−30+3)5B=(−7−1333)B=15(−7−1333)

If $3 A - 2 B = (\begin{matrix} 1 & - 2 3 & 0 \end{matrix})$ and $2 A - 3 B = (\begin{matrix} - 3 & 3 1 & - 1 \end{matrix})$ then find $B$