If A - - 0 1 2- 2 3 4- 4 5 -6 - B- -1 2 3- 0 1 0- 0 0 -1 - find 4A-6B-

The correct option is B [ 6 amp; 8 amp; 10; 8 amp;6 amp;16; 16 amp;20 amp; 18 ] Given, A=[ 0 amp; 1 amp; 2; 2 am ...

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Standard XII

Mathematics

Scalar Multiplication of a Matrix

If A = [ 0 ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 2 2 & 3 & 4 4 & 5 & - 6 \end{matrix} ⎤ ⎥ ⎦$ , $B = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 0 & 1 & 0 0 & 0 & - 1 \end{matrix} ⎤ ⎥ ⎦,$ find $4 A - 6 B$ .

⎡ ⎢ ⎣ \begin{matrix} 4 & 1 & - 2 8 & 20 & 18 16 & 20 & 18 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 6 & - 8 & - 10 8 & 6 & 16 16 & 20 & - 18 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} - 6 & - 1 & - 10 8 & - 6 & 16 16 & - 20 & - 18 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} - 6 & - 8 & 10 - 8 & 6 & 16 16 & 20 & - 18 \end{matrix} ⎤ ⎥ ⎦

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Solution

The correct option is B $⎡ ⎢ ⎣ \begin{matrix} 6 & - 8 & - 10 8 & 6 & 16 16 & 20 & - 18 \end{matrix} ⎤ ⎥ ⎦$
Given, $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 2 2 & 3 & 4 4 & 5 & - 6 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 0 & 1 & 0 0 & 0 & - 1 \end{matrix} ⎤ ⎥ ⎦$

$∴ 4 A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 4 & 8 8 & 12 & 16 16 & 20 & - 24 \end{matrix} ⎤ ⎥ ⎦$ and $6 B = ⎡ ⎢ ⎣ \begin{matrix} - 6 & 12 & 8 0 & 6 & 0 0 & 0 & - 6 \end{matrix} ⎤ ⎥ ⎦$

$\Rightarrow 4 A - 6 B = ⎡ ⎢ ⎣ \begin{matrix} 0 - (- 6) & 4 - 12 & 8 - 18 8 - 0 & 12 - 6 & 16 - 0 16 - 0 & 20 - 0 & - 24 - (- 6) \end{matrix} ⎤ ⎥ ⎦$

$\Rightarrow 4 A - 6 B = ⎡ ⎢ ⎣ \begin{matrix} 6 & - 8 & - 10 8 & 6 & 16 16 & 20 & - 18 \end{matrix} ⎤ ⎥ ⎦$
$∴$ Option B is the correct answer.

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If A=⎡⎢⎣01223445−6⎤⎥⎦, B=⎡⎢⎣−12301000−1⎤⎥⎦, find 4A−6B.

If $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & 2 2 & 3 & 4 4 & 5 & - 6 \end{matrix} ⎤ ⎥ ⎦$ , $B = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 0 & 1 & 0 0 & 0 & - 1 \end{matrix} ⎤ ⎥ ⎦,$ find $4 A - 6 B$ .