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Mathematics

If A = [−3−70−8] and A−B=[64−30]\begin{bmatrix}[r] -3 & -7 \ 0 & -8 \end{bmatrix}\text{ and } A - B = \begin{bmatrix}[r] 6 & 4 \ -3 & 0 \end{bmatrix}, then matrix B is :

  1. [911−318]\begin{bmatrix}[r] 9 & 11 \ -3 & 18 \end{bmatrix}

  2. [−9−1138]\begin{bmatrix}[r] -9 & -11 \ 3 & 8 \end{bmatrix}

  3. [9−11−38]\begin{bmatrix}[r] 9 & -11 \ -3 & 8 \end{bmatrix}

  4. [−9−11−3−8]\begin{bmatrix}[r] -9 & -11 \ -3 & -8 \end{bmatrix}

Matrices

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Answer

Given,

A - B = [64−30]\begin{bmatrix}[r] 6 & 4 \ -3 & 0 \end{bmatrix}

Substituting value of A in above equation we get :

⇒[−3−70−8]−B=[64−30]⇒B=[−3−70−8]−[64−30]⇒B=[−3−6−7−40−(−3)−8−0]⇒B=[−9−113−8]\Rightarrow \begin{bmatrix}[r] -3 & -7 \ 0 & -8 \end{bmatrix} - B = \begin{bmatrix}[r] 6 & 4 \ -3 & 0 \end{bmatrix} \\[1em] \Rightarrow B = \begin{bmatrix}[r] -3 & -7 \ 0 & -8 \end{bmatrix} - \begin{bmatrix}[r] 6 & 4 \ -3 & 0 \end{bmatrix} \\[1em] \Rightarrow B = \begin{bmatrix}[r] -3 - 6 & -7 - 4 \ 0 - (-3) & -8 - 0 \end{bmatrix} \\[1em] \Rightarrow B = \begin{bmatrix}[r] -9 & -11 \ 3 & -8 \end{bmatrix}

Hence, Option 4 is the correct option.

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