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Mathematics

If M = [01] and N=[10]\begin{bmatrix}[r] 0 \ 1 \end{bmatrix} \text{ and N} = \begin{bmatrix}[r] 1 \ 0 \end{bmatrix}, show that :

3M + 5N = [53]\begin{bmatrix}[r] 5 \ 3 \end{bmatrix}

Matrices

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Answer

Substituting value of M and N in 3M + 5N we get,

⇒3M+5N=3[01]+5[10]=[03]+[50]=[53].\Rightarrow 3M + 5N = 3\begin{bmatrix}[r] 0 \ 1 \end{bmatrix} + 5\begin{bmatrix}[r] 1 \ 0 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 0 \ 3 \end{bmatrix} + \begin{bmatrix}[r] 5 \ 0 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 5 \ 3 \end{bmatrix}.

Hence, proved that 3M + 5N = [53]\begin{bmatrix}[r] 5 \ 3 \end{bmatrix}.

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