Question

1. use determinants to find if the matrix has an inverse. select yes or no. \\(\begin{bmatrix}4 & 2 \\ 6 & 3end{bmatrix}\\) \\(\circ\\) yes \\(\circ\\) no 4) use determinants to find if the matrix has an inverse. select yes or no. \\(\begin{bmatrix}1 & 2 \\ 5 & 3end{bmatrix}\\) \\(\circ\\) yes \\(\circ\\) no 5) use determinants to find if the matrix has an inverse. select yes or no. \\(\begin{bmatrix}0 & 1 \\ 7 & -6end{bmatrix}\\) \\(\circ\\) no \\(\circ\\) yes

Explanation:

Question 3

Step1: Recall determinant formula for 2x2 matrix

For a matrix

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

, the determinant is $ad - bc$.

Step2: Calculate determinant of given matrix

Given matrix

$$\begin{bmatrix}4&2\\6&3\end{bmatrix}$$

, $a = 4$, $b = 2$, $c = 6$, $d = 3$.
Determinant = $4\times3 - 2\times6 = 12 - 12 = 0$.

Step3: Determine inverse existence

A matrix has an inverse if and only if its determinant is non - zero. Since the determinant is 0, the matrix has no inverse.

Step1: Recall determinant formula for 2x2 matrix

For a matrix

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

, the determinant is $ad - bc$.

Step2: Calculate determinant of given matrix

Given matrix

$$\begin{bmatrix}1&2\\5&3\end{bmatrix}$$

, $a = 1$, $b = 2$, $c = 5$, $d = 3$.
Determinant = $1\times3 - 2\times5 = 3 - 10=- 7$.

Step3: Determine inverse existence

A matrix has an inverse if and only if its determinant is non - zero. Since the determinant ($-7$) is non - zero, the matrix has an inverse.

Step1: Recall determinant formula for 2x2 matrix

For a matrix

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

, the determinant is $ad - bc$.

Step2: Calculate determinant of given matrix

Given matrix

$$\begin{bmatrix}0&1\\7&- 6\end{bmatrix}$$

, $a = 0$, $b = 1$, $c = 7$, $d=-6$.
Determinant = $0\times(-6)-1\times7 = 0 - 7=-7$.

Step3: Determine inverse existence

A matrix has an inverse if and only if its determinant is non - zero. Since the determinant ($-7$) is non - zero, the matrix has an inverse.

Answer:

no

Question 4