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Mathematics

The additive inverse of matrix A + B, where

A = [427−2] and B=[−213−4]\begin{bmatrix}[r] 4 & 2 \ 7 & -2 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] -2 & 1 \ 3 & -4 \end{bmatrix} is :

  1. [−2−3−106]\begin{bmatrix}[r] -2 & -3 \ -10 & 6 \end{bmatrix}

  2. [23−10−6]\begin{bmatrix}[r] 2 & 3 \ -10 & -6 \end{bmatrix}

  3. [−2−3−10−6]\begin{bmatrix}[r] -2 & -3 \ -10 & -6 \end{bmatrix}

  4. [−2310−6]\begin{bmatrix}[r] -2 & 3 \ 10 & -6 \end{bmatrix}

Matrices

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Answer

Additive inverse of a matrix M is given by -M.

So, additive inverse of (A + B) = -(A + B).

Substituting values we get :

⇒−(A+B)=−([427−2]+[−213−4])=−([4+(−2)2+17+3−2+(−4)])=−([2310−6])=[−2−3−106]\Rightarrow -(A + B) = -\Big(\begin{bmatrix}[r] 4 & 2 \ 7 & -2 \end{bmatrix} + \begin{bmatrix}[r] -2 & 1 \ 3 & -4 \end{bmatrix}\Big) \\[1em] = -\Big(\begin{bmatrix}[r] 4 + (-2) & 2 + 1 \ 7 + 3 & -2 + (-4) \end{bmatrix}\Big) \\[1em] = -\Big(\begin{bmatrix}[r] 2 & 3 \ 10 & -6 \end{bmatrix}\Big) \\[1em] = \begin{bmatrix}[r] -2 & -3 \ -10 & 6 \end{bmatrix}

Hence, Option 1 is the correct option.

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