Problem

Find the result of the scalar 5 multiplied by the 2x2 identity matrix.

Answer

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Answer

The final result is a matrix where each element of the identity matrix has been multiplied by 5: \(5I = \begin{bmatrix}5 & 0\\0 & 5\end{bmatrix}\).

Steps

Step 1 ：The 2x2 identity matrix is \(I = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\).

Step 2 ：To multiply a matrix by a scalar, we multiply each element of the matrix by that scalar, resulting in \(5I = \begin{bmatrix}5 * 1 & 5 * 0\\5 * 0 & 5 * 1\end{bmatrix}\).

Step 3 ：The final result is a matrix where each element of the identity matrix has been multiplied by 5: \(5I = \begin{bmatrix}5 & 0\\0 & 5\end{bmatrix}\).

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