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Mathematics

Find the matrix A, if A + [46−37]\begin{bmatrix} 4 & 6 \ -3 & 7 \end{bmatrix} = [3−65−8]\begin{bmatrix} 3 & -6 \ 5 & -8 \end{bmatrix}

  1. [−1128−15]\begin{bmatrix} -1 & 12 \ 8 & -15 \end{bmatrix}

  2. [−1−128−15]\begin{bmatrix} -1 & -12 \ 8 & -15 \end{bmatrix}

  3. [−1−12−8−15]\begin{bmatrix} -1 & -12 \ -8 & -15 \end{bmatrix}

  4. [112815]\begin{bmatrix} 1 & 12 \ 8 & 15 \end{bmatrix}

Matrices

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Answer

Given,

A + [46−37]\begin{bmatrix} 4 & 6 \ -3 & 7 \end{bmatrix} = [3−65−8]\begin{bmatrix} 3 & -6 \ 5 & -8 \end{bmatrix}

Solving for A:

⇒A=[3−65−8]−[46−37]=[3−4−6−65−(−3)−8−7]=[−1−128−15]\Rightarrow A = \begin{bmatrix} 3 & -6 \ 5 & -8 \end{bmatrix} - \begin{bmatrix} 4 & 6 \ -3 & 7 \end{bmatrix} \\[1em] = \begin{bmatrix} 3 - 4 & -6 - 6 \ 5 - (-3) & -8 - 7 \end{bmatrix} \\[1em] = \begin{bmatrix} -1 & -12 \ 8 & -15 \end{bmatrix}

Hence, option 2 is the correct option.

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