QuestionPart 1 Find the determinant of the following matrix: $$\left[\begin{array}{cc} 8 & 18 \\ -3 & 2 \end{array}\right]$$
70 - Part 2
Does this matrix have an inverse? $\checkmark$ A. Yes B. No
Part 3 Find the inverse of the matrix. $\square$
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Studdy Solution
Find the inverse of the matrix $\begin{bmatrix} 8 & 18 \\ -3 & 2 \end{bmatrix}$.
The inverse is given by:
$$\frac{1}{70} \begin{bmatrix} 2 & -18 \\ 3 & 8 \end{bmatrix}$$
$$= \begin{bmatrix} \frac{2}{70} & \frac{-18}{70} \\ \frac{3}{70} & \frac{8}{70} \end{bmatrix}$$
Simplify the fractions:
$$= \begin{bmatrix} \frac{1}{35} & \frac{-9}{35} \\ \frac{3}{70} & \frac{4}{35} \end{bmatrix}$$
The inverse of the matrix is:
$$\begin{bmatrix} \frac{1}{35} & \frac{-9}{35} \\ \frac{3}{70} & \frac{4}{35} \end{bmatrix}$$