what is the product?\n3·\\(\\begin{bmatrix}-6&-11\\\\-14&-9\\end{bmatrix}\\)\n\\(\\begin{bmatrix}-3&-8\\\\-11…

Explanation:

Step1: Multiply scalar by matrix elements

When multiplying a scalar (k = 3) by a matrix (\begin{bmatrix}a&b\c&d\end{bmatrix}), we use the rule (k\begin{bmatrix}a&b\c&d\end{bmatrix}=\begin{bmatrix}ka&kb\kc&kd\end{bmatrix}). Here (a=-6), (b = - 11), (c=-14), (d=-9).

Step2: Calculate each element

For the top - left element: (3\times(-6)=-18). For the top - right element: (3\times(-11)=-33). For the bottom - left element: (3\times(-14)=-42). For the bottom - right element: (3\times(-9)=-27).

Answer:

(\begin{bmatrix}-18&-33\-42&-27\end{bmatrix})