find the inverse of the matrix below.\n \begin{bmatrix} 14 & 5 \\ 6 & 3 end{bmatrix} \nif necessary, round…

Explanation:

Step1: Calculate the determinant

For a matrix (A=\begin{bmatrix}a&b\c&d\end{bmatrix}), the determinant (det(A)=ad - bc). Here (a = 14), (b = 5), (c = 6), (d = 3). (det(A)=14\times3-5\times6=42 - 30=12)

Step2: Use the formula for the inverse of a (2\times2) matrix

The inverse of (A=\begin{bmatrix}a&b\c&d\end{bmatrix}) is (A^{-1}=\frac{1}{det(A)}\begin{bmatrix}d&-b\-c&a\end{bmatrix}) Substitute (a = 14), (b = 5), (c = 6), (d = 3) and (det(A)=12) (A^{-1}=\frac{1}{12}\begin{bmatrix}3&- 5\-6&14\end{bmatrix}=\begin{bmatrix}\frac{3}{12}&\frac{-5}{12}\\frac{-6}{12}&\frac{14}{12}\end{bmatrix}=\begin{bmatrix}0.25&-0.42\-0.5&1.17\end{bmatrix}) (rounded to the nearest hundredth)

Answer:

(\begin{bmatrix}0.25&-0.42\-0.5&1.17\end{bmatrix})