Compute the indicated product- beginbmatrix1 W2113lendbmatrix - 2 - 3 - 4 -

[ 1; 2; 3 ]_3 × 1 [2 3 4]_1 × 3 =[ 1 × 2 amp; 1 × 3 amp; 1 × 4; 2 × 2 amp; 2 × 3 amp; 2 × 4; 3 × 2 amp; 3 × 3 amp; 3 × 4 ]_3 × 3 =[ 2 ...

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Standard XII

Mathematics

Inverse of a Matrix

Compute the i...

Question

Compute the indicated product.
$⎡ ⎢ ⎣ \begin{matrix} 123 \end{matrix} ⎤ ⎥ ⎦ [234]$

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Solution

${⎡ ⎢ ⎣ \begin{matrix} 123 \end{matrix} ⎤ ⎥ ⎦}_{3 \times 1} [234]_{1 \times 3} = {⎡ ⎢ ⎣ \begin{matrix} 1 \times 2 & 1 \times 3 & 1 \times 4 2 \times 2 & 2 \times 3 & 2 \times 4 3 \times 2 & 3 \times 3 & 3 \times 4 \end{matrix} ⎤ ⎥ ⎦}_{3 \times 3} = ⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 4 4 & 6 & 8 6 & 9 & 12 \end{matrix} ⎤ ⎥ ⎦$

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

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

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

Q. 3.Compute the indicated products,()212 3 4()21 -211 2 3]3 2 3 111) D2 1(v) 3 22 3 413 54 5 6 3 0 53-1 3(iv) 3 4 50 2 41V(vi)-1 0 2-」131

Q. Compute the indicated products:
(i)

[\begin{matrix} a & b \\ - b & a \end{matrix}] [\begin{matrix} a & - b \\ b & a \end{matrix}]

(ii)

[\begin{matrix} 1 & - 2 \\ 2 & 3 \end{matrix}] [\begin{matrix} 1 & 2 & 3 \\ - 3 & 2 & - 1 \end{matrix}]

(iii)

[\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}]

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Compute the indicated product. ⎡⎢⎣123⎤⎥⎦[2 3 4]

⎡⎢⎣123⎤⎥⎦3×1[2 3 4]1×3=⎡⎢⎣1×21×31×42×22×32×43×23×33×4⎤⎥⎦3×3=⎡⎢⎣2344686912⎤⎥⎦

Compute the indicated product.
$⎡ ⎢ ⎣ \begin{matrix} 123 \end{matrix} ⎤ ⎥ ⎦ [234]$