Given- for a matrix- B- beginbmatrix 2 -3 - 511 -2 - 3 -8111-3-0bmatrix - - what will be its additive inverse-

The correct option is D [ 2 amp;3 amp; 5; 2 amp; 3 amp;8; 1 amp; 3 amp;0 ] nbsp;If B be any given matrix then –B is the additive inverse of ...

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Standard X

Mathematics

Additive Identity and Additive Inverse of a Matrix

Given, for a ...

Question

Given, for a matrix
$B = ⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 & 5 - 2 & 3 & - 8 1 & 3 & 0 \end{matrix} ⎤ ⎥ ⎦,$
what will be its additive inverse?

⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 & 5 - 2 & 3 & - 8 1 & 3 & 0 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 0 & 0 & 0 0 & 0 & 0 0 & 0 & 0 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} - 2 & 3 & - 5 2 & - 3 & 8 - 1 & - 3 & 0 \end{matrix} ⎤ ⎥ ⎦

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⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦

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Solution

The correct option is C $⎡ ⎢ ⎣ \begin{matrix} - 2 & 3 & - 5 2 & - 3 & 8 - 1 & - 3 & 0 \end{matrix} ⎤ ⎥ ⎦$
If B be any given matrix then –B is the additive inverse of B.
In fact we have $B + (- B) = (- B) + B = O$

$∴ - (B) = ⎡ ⎢ ⎣ \begin{matrix} - 2 & - (- 3) & - 5 - (- 2) & - 3 & - (- 8) - 1 & - 3 & 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 2 & 3 & - 5 2 & - 3 & 8 - 1 & - 3 & 0 \end{matrix} ⎤ ⎥ ⎦$

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Given, for a matrix B=⎡⎢⎣2−35−23−8130⎤⎥⎦, what will be its additive inverse?

The correct option is C ⎡⎢⎣−23−52−38−1−30⎤⎥⎦ If B be any given matrix then –B is the additive inverse of B. In fact we have B+(−B)=(−B)+B=O ∴−(B)=⎡⎢⎣−2−(−3)−5−(−2)−3−(−8)−1−30⎤⎥⎦ =⎡⎢⎣−23−52−38−1−30⎤⎥⎦

Given, for a matrix
$B = ⎡ ⎢ ⎣ \begin{matrix} 2 & - 3 & 5 - 2 & 3 & - 8 1 & 3 & 0 \end{matrix} ⎤ ⎥ ⎦,$
what will be its additive inverse?