If H - beginbmatrix 18283 12 - 3 - 11181 - 2lend bmatrix G - beginbmatrix 8 -10 0 -4 - 811-8 84Find 3 H -1-2 GA- 283 - 1411- 11- 7 - 4 lendbmatrix B- beginbmatrix 283 - 1411- 0 - 1118 - 7 - 4lendbmatrix C- b e g i n b m a t r i x -2 - 8 - 2 1- 11 -1 8 - 7 - 4 e n d b m a t r i x D- beginbmatrix 2 - 3 - 14

The correct option is A [ 2 amp;3 amp;14; 6 amp; 11 amp; 1; 8 amp; 7 amp; 4 ] Given H=[ 1 amp;2 amp;3; 2 amp; 3 amp; 1; ...

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Byju's Answer

Standard X

Mathematics

Scalar Multiplication of a Matrix

If H = beginb...

Question

If $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦ G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$

Find $3 H - \frac{1}{2} G$

$⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 14 6 & 11 & - 1 8 & 7 & 4 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 14 1 & 0 & 1 8 & 7 & 4 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} - 2 & 8 & 2 6 & 11 & - 1 8 & 7 & 4 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 14 6 & 11 & - 1 3 & 0 & - 2 \end{matrix} ⎤ ⎥ ⎦$

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Solution

The correct option is A
$⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 14 6 & 11 & - 1 8 & 7 & 4 \end{matrix} ⎤ ⎥ ⎦$

Given $H = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦ G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & - 10 0 & - 4 & 8 2 & - 8 & 4 \end{matrix} ⎤ ⎥ ⎦$

$3 H = ⎡ ⎢ ⎣ \begin{matrix} 3 \times 1 & 3 \times 2 & 3 \times 3 3 \times 2 & 3 \times 3 & 3 \times 1 3 \times 3 & 3 \times 1 & 3 \times 2 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 3 & 6 & 9 6 & 9 & 3 9 & 3 & 6 \end{matrix} ⎤ ⎥ ⎦$

$\frac{1}{2} G = ⎡ ⎢ ⎣ \begin{matrix} 2 \div 2 & 6 \div 2 & - 10 \div 2 0 \div 2 & - 4 \div 2 & 8 \div 2 2 \div 2 & - 8 \div 2 & 4 \div 2 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 3 & - 5 0 & - 2 & 4 1 & - 4 & 2 \end{matrix} ⎤ ⎥ ⎦$

$3 H - \frac{1}{2} G = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 14 6 & 11 & - 1 8 & 7 & 4 \end{matrix} ⎤ ⎥ ⎦$

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If H=⎡⎢⎣123231312⎤⎥⎦G=⎡⎢⎣26−100−482−84⎤⎥⎦ Find 3H−12G

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