Compute the indicated product- beginbmatrix 38-1 - 31-1 - 0 - 211lend bmatrix beginbmatrix 2 -3111 - 0 13 - 1lendbmatrix

[ 3 amp; 1 amp; 3; 1 amp; 0 amp; 2; ][ 2 amp; 3; 1 amp; 0; 3 amp; 1 ] =[ 6 1+9 amp; 9+0+3; 2+0+6 amp; ...

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Standard XII

Mathematics

Scalar Multiplication of a Matrix

Compute the i...

Question

Compute the indicated product.
$[\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}]$ $⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 1 & 0 3 & 1 \end{matrix} ⎤ ⎥ ⎦$

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Solution

$[\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}] ⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 1 & 0 3 & 1 \end{matrix} ⎤ ⎥ ⎦ = [\begin{matrix} 6 - 1 + 9 & - 9 + 0 + 3 - 2 + 0 + 6 & 3 + 0 + 2 \end{matrix}] = [\begin{matrix} 14 & - 6 4 & 5 \end{matrix}]$

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Compute the indicated product
$⎡ ⎢ ⎣ \begin{matrix} 2 & 1 3 & 2 - 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{matrix} 1 & 0 & 1 - 1 & 2 & 1 \end{matrix}]$

Compute the indicated product.
$[\begin{matrix} 1 & - 2 2 & 3 \end{matrix}]$ $[\begin{matrix} 1 & 2 & 3 2 & 3 & 1 \end{matrix}]$

Compute the indicated product.
$⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 4 3 & 4 & 5 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦$ $⎡ ⎢ ⎣ \begin{matrix} 1 & - 3 & 5 0 & 2 & 4 3 & 0 & 5 \end{matrix} ⎤ ⎥ ⎦$

Compute the indicated products.
$(i) [\begin{matrix} a & b - b & a \end{matrix}] [\begin{matrix} a & - b b & a \end{matrix}]$

$(i i) ⎡ ⎢ ⎣ \begin{matrix} 123 \end{matrix} ⎤ ⎥ ⎦ [234]$

$(i i i) [\begin{matrix} 1 & - 2 2 & 3 \end{matrix}] [\begin{matrix} 1 & 2 & 3 2 & 3 & 1 \end{matrix}]$

$(i v) ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 4 3 & 4 & 5 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 1 & - 3 & 5 0 & 2 & 4 3 & 0 & 5 \end{matrix} ⎤ ⎥ ⎦$

$(v) ⎡ ⎢ ⎣ \begin{matrix} 2 & 1 3 & 2 - 1 & 1 \end{matrix} ⎤ ⎥ ⎦ [\begin{matrix} 1 & 0 & 1 - 1 & 2 & 1 \end{matrix}]$

$(v i) [\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}] ⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 1 & 0 3 & 1 \end{matrix} ⎤ ⎥ ⎦$

Q. If

A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & 1 & \frac{5}{3} \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \frac{7}{3} & 2 & \frac{2}{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦ B = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{3} & \frac{3}{5} & 1 \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦

then compute 3A-5B

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Compute the indicated product. [3−13−102]⎡⎢⎣2−31031⎤⎥⎦

[3−13−102]⎡⎢⎣2−31031⎤⎥⎦=[6−1+9−9+0+3−2+0+63+0+2]=[14−645]

Compute the indicated product.
$[\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}]$ $⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 1 & 0 3 & 1 \end{matrix} ⎤ ⎥ ⎦$

$[\begin{matrix} 3 & - 1 & 3 - 1 & 0 & 2 \end{matrix}] ⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 1 & 0 3 & 1 \end{matrix} ⎤ ⎥ ⎦ = [\begin{matrix} 6 - 1 + 9 & - 9 + 0 + 3 - 2 + 0 + 6 & 3 + 0 + 2 \end{matrix}] = [\begin{matrix} 14 & - 6 4 & 5 \end{matrix}]$