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Mathematics

If A = [5540],B=[3214] and C=[2321]\begin{bmatrix}[r] 5 & 5 \ 4 & 0 \end{bmatrix}, B = \begin{bmatrix}[r] 3 & 2 \ 1 & 4 \end{bmatrix} \text{ and } C = \begin{bmatrix}[r] -2 & 3 \ 2 & 1 \end{bmatrix} then matrix (A + B - C) is :

  1. [10433]\begin{bmatrix}[r] 10 & 4 \ -3 & 3 \end{bmatrix}

  2. [10433]\begin{bmatrix}[r] -10 & 4 \ 3 & -3 \end{bmatrix}

  3. [10433]\begin{bmatrix}[r] 10 & 4 \ 3 & 3 \end{bmatrix}

  4. [10433]\begin{bmatrix}[r] 10 & -4 \ 3 & 3 \end{bmatrix}

Matrices

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Answer

Given,

A = [5540],B=[3214] and C=[2321]\begin{bmatrix}[r] 5 & 5 \ 4 & 0 \end{bmatrix}, B = \begin{bmatrix}[r] 3 & 2 \ 1 & 4 \end{bmatrix} \text{ and } C = \begin{bmatrix}[r] -2 & 3 \ 2 & 1 \end{bmatrix}

(A+BC)=[5540]+[3214][2321]=[5+3(2)5+234+120+41]=[8+2735241]=[10433].(A + B - C) = \begin{bmatrix}[r] 5 & 5 \ 4 & 0 \end{bmatrix} + \begin{bmatrix}[r] 3 & 2 \ 1 & 4 \end{bmatrix} - \begin{bmatrix}[r] -2 & 3 \ 2 & 1 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 5 + 3 - (-2) & 5 + 2 - 3 \ 4 + 1 - 2 & 0 + 4 - 1 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 8 + 2 & 7 - 3 \ 5 - 2 & 4 - 1 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 10 & 4 \ 3 & 3 \end{bmatrix}.

Hence, Option 3 is the correct option.

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