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Mathematics

If A = [5103−4]\begin{bmatrix} 5 & 10 \ 3 & -4 \end{bmatrix} and I = [1001]\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}, then AI is equal to:

  1. [1001]\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}

  2. [510−34]\begin{bmatrix} 5 & 10 \ -3 & 4 \end{bmatrix}

  3. [5103−4]\begin{bmatrix} 5 & 10 \ 3 & -4 \end{bmatrix}

  4. [1515−1−1]\begin{bmatrix} 15 & 15 \ -1 & -1 \end{bmatrix}

Matrices

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Answer

Given,

A = [5103−4]\begin{bmatrix} 5 & 10 \ 3 & -4 \end{bmatrix} and I = [1001]\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}

Solving for AI:

⇒[5103−4]×[1001]⇒[5(1)+10(0)5(0)+10(1)3(1)+(−4)(0)3(0)+(−4)(1)]⇒[5+00+103+00+(−4)]⇒[5103−4].\Rightarrow \begin{bmatrix} 5 & 10 \ 3 & -4 \end{bmatrix} \times \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 5(1) + 10(0) & 5(0) + 10(1) \ 3(1) + (-4)(0) & 3(0) + (-4)(1) \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 5 + 0 & 0 + 10 \ 3 + 0 & 0 + (-4) \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 5 & 10 \ 3 & -4 \end{bmatrix}.

Hence, option 3 is the correct option.

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