Question

part 2: find the determinant of each matrix. show all work to receive full credit!

1. \\( \

$$\begin{bmatrix} 4 & 3 \\\\ -1 & -1 \\end{bmatrix}$$

\\)

1. \\( \

$$\begin{bmatrix} -4 & 2 \\\\ 0 & -4 \\end{bmatrix}$$

\\)

Explanation:

Problem 7:

Step1: Recall determinant formula

For a \( 2\times2 \) matrix \(

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

\), determinant is \( ad - bc \).

Step2: Apply formula to given matrix

Matrix: \(

$$\begin{bmatrix} 4 & 3 \\ -1 & -1 \end{bmatrix}$$

\), so \( a = 4, b = 3, c = -1, d = -1 \).
Determinant \( = (4)(-1) - (3)(-1) = -4 + 3 = -1 \).

Problem 8:

Step1: Recall determinant formula

For \( 2\times2 \) matrix \(

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

\), determinant is \( ad - bc \).

Step2: Apply formula to given matrix

Matrix: \(

$$\begin{bmatrix} -4 & 2 \\ 0 & -4 \end{bmatrix}$$

\), so \( a = -4, b = 2, c = 0, d = -4 \).
Determinant \( = (-4)(-4) - (2)(0) = 16 - 0 = 16 \).

Answer:

Problem 7: \(-1\)
Problem 8: \(16\)