Question

1. find the determinant to determine if the matrix has an inverse. select yes or no.\

$$\begin{bmatrix}2&10\\\\1&5\\end{bmatrix}$$

yesnono\\ \\3. select yes if the determinant shows that the matrix will reduce to an identity matrix; select no if it does not.\

$$\begin{bmatrix}3&0\\\\5&1\\end{bmatrix}$$

yesno

Explanation:

Question 2

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

$$\begin{bmatrix}2&10\\1&5\end{bmatrix}$$

, so $a = 2$, $b = 10$, $c = 1$, $d = 5$.
Determinant = $2\times5 - 10\times1 = 10 - 10 = 0$.

Step3: Determine invertibility

A matrix has an inverse if and only if its determinant is non - zero. Since the determinant is 0, the matrix does not have 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

$$\begin{bmatrix}3&0\\5&1\end{bmatrix}$$

, so $a = 3$, $b = 0$, $c = 5$, $d = 1$.
Determinant = $3\times1 - 0\times5 = 3 - 0 = 3$.

Step3: Determine if it reduces to identity matrix

A matrix with a non - zero determinant is invertible, and an invertible matrix can be reduced to the identity matrix using row operations. Since the determinant is 3 (non - zero), the matrix will reduce to an identity matrix.

Answer:

no

Question 3