Matrix Problem-Solving 2: Determinants and Inverses

Matrix Problem-Solving 2: Determinants and Inverses

Problem Set

Find the determinant of the following matrices:

$$A = \begin{pmatrix} 3 & 8 \\ 4 & 6 \end{pmatrix}$$

$$B = \begin{pmatrix} 7 & 5 \\ 2 & 1 \end{pmatrix}$$

$$C = \begin{pmatrix} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 1 & 2 & 1 \end{pmatrix}$$

$$D = \begin{pmatrix} 4 & 3 \\ 2 & 5 \end{pmatrix}$$

$$E = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$$

$$F = \begin{pmatrix} 6 & 7 \\ 3 & 9 \end{pmatrix}$$

$$G = \begin{pmatrix} 5 & 8 & 3 \\ 2 & 7 & 1 \\ 9 & 6 & 4 \end{pmatrix}$$

$$H = \begin{pmatrix} 2 & 0 & 1 \\ 3 & 4 & 1 \\ 1 & 2 & 3 \end{pmatrix}$$

$$I = \begin{pmatrix} 7 & 4 \\ 3 & 5 \end{pmatrix}$$

$$J = \begin{pmatrix} 2 & 1 \\ 6 & 3 \end{pmatrix}$$

Find the inverse of the following matrices (if it exists):

$$K = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$

$$L = \begin{pmatrix} 5 & 2 \\ 1 & 3 \end{pmatrix}$$

$$M = \begin{pmatrix} 4 & 3 \\ 3 & 2 \end{pmatrix}$$

$$N = \begin{pmatrix} 7 & 8 \\ 9 & 10 \end{pmatrix}$$

$$O = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$$

$$P = \begin{pmatrix} 3 & 5 \\ 7 & 2 \end{pmatrix}$$

$$Q = \begin{pmatrix} 8 & 3 \\ 4 & 6 \end{pmatrix}$$

$$R = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}$$

$$S = \begin{pmatrix} 4 & 7 \\ 1 & 5 \end{pmatrix}$$

$$T = \begin{pmatrix} 9 & 3 \\ 6 & 2 \end{pmatrix}$$

Solve the system of linear equations using the inverse matrix method:

$$\begin{aligned} 2x + 3y &= 5 \\ 4x + y &= 6 \end{aligned}$$

$$\begin{aligned} x + 2y &= 7 \\ 3x - y &= 5 \end{aligned}$$
$$\begin{aligned} 3x - 4y &= 2 \\ 2x + 5y &= 1 \end{aligned}$$

$$\begin{aligned} x - y &= 3 \\ x + y &= 5 \end{aligned}$$

$$\begin{aligned} 4x + 3y &= 8 \\ x - 2y &= 2 \end{aligned}$$