If A - lbegin bmatrix 2 - 8 -4 10 -1 -2 13 -1 - 5lend bmatrix Find A - A -A- beginbmatrix 488 -1118 -2 -3 18-3 - 10 e n d b m a t r i x B- Vbeginbmatrix 488 - 111882 - 3 183 - 10 e n d b m a t r i x C- beginbmatrix 488 -1118 - 6 -3 185 - 10 e n d b m a t r i x D- beginbmatrix 488 -18-2 -3 10 -1 - 9 e n d b m a t r i x

The correct option is A [ 4 amp; 8 amp; 1; 8 amp; 2 amp; 3; 1 amp; 3 amp; 10 ] Transpose of a matrix is obtained by interchanging the ro ...

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Byju's Answer

Standard X

Mathematics

Transpose of a Matrix

If A = lbegin...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 8 & - 4 0 & - 1 & - 2 3 & - 1 & 5 \end{matrix} ⎤ ⎥ ⎦$ Find A+A'

$⎡ ⎢ ⎣ \begin{matrix} 4 & 8 & - 1 8 & - 2 & - 3 - 1 & - 3 & 10 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 4 & 8 & 1 8 & 2 & 3 1 & 3 & 10 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 4 & 8 & - 1 8 & 6 & - 3 1 & 5 & 10 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 4 & 8 & - 1 8 & - 2 & - 3 0 & - 1 & 9 \end{matrix} ⎤ ⎥ ⎦$

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Solution

The correct option is A
$⎡ ⎢ ⎣ \begin{matrix} 4 & 8 & - 1 8 & - 2 & - 3 - 1 & - 3 & 10 \end{matrix} ⎤ ⎥ ⎦$

Transpose of a matrix is obtained by interchanging the rows and columns.

$A^{'} = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 3 8 & - 1 & - 1 - 4 & - 2 & 5 \end{matrix} ⎤ ⎥ ⎦$

$A + A^{'} = ⎡ ⎢ ⎣ \begin{matrix} 2 + 2 & 8 + 0 & - 4 + 3 0 + 8 & - 1 - 1 & - 2 - 1 3 - 4 & - 1 - 2 & 5 + 5 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 4 & 8 & - 1 8 & - 2 & - 3 - 1 & - 3 & 10 \end{matrix} ⎤ ⎥ ⎦$

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