Problem

If \( A = \begin{bmatrix} 2 & 4\\ 1 & 3\end{bmatrix} \), find the result of the scalar multiplication \( 5A \).

Answer

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Answer

Simplifying that, we get the final answer: \( 5A = \begin{bmatrix} 10 & 20\\ 5 & 15\end{bmatrix} \)

Steps

Step 1 ：Firstly, we write down the matrix A: \( A = \begin{bmatrix} 2 & 4\\ 1 & 3\end{bmatrix} \).

Step 2 ：Scalar multiplication involves multiplying every entry of the matrix by the scalar. So, we multiply every entry of A by 5: \( 5A = 5 * \begin{bmatrix} 2 & 4\\ 1 & 3\end{bmatrix} \)

Step 3 ：Carrying out the multiplication gives us: \( 5A = \begin{bmatrix} 5*2 & 5*4\\ 5*1 & 5*3\end{bmatrix} \)

Step 4 ：Simplifying that, we get the final answer: \( 5A = \begin{bmatrix} 10 & 20\\ 5 & 15\end{bmatrix} \)

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