Chapter 4.5, Problem 60HP

(a)

To determine

To find: The2x2 matrix when the determinant is 0.

Answer to Problem 60HP

The 2x2 matrix when the determinant is 0 is $\left[\begin{array}{cc}2& 4\\ 1& 2\end{array}\right]$ .

Explanation of Solution

Given, The determinant is 0.

Calculation:

Calculate the matrix.

  $\begin{array}{c}\left[\begin{array}{cc}2& 4\\ 1& 2\end{array}\right]=2\left(2\right)-\left(4\right)\left(1\right)\\ =4-4\\ =0\end{array}$

Thus, the 2x2 matrix when the determinant is 0 is $\left[\begin{array}{cc}2& 4\\ 1& 2\end{array}\right]$ .

(b)

To determine

The 2x2 matrix when the determinant is 25.

Answer to Problem 60HP

The 2x2 matrix when the determinant is 25 is $\left[\begin{array}{cc}3& 4\\ -4& 3\end{array}\right]$ .

Explanation of Solution

Given, The determinant is 25.

Calculation:

Calculate the matrix.

  $\begin{array}{c}\left[\begin{array}{cc}3& 4\\ -4& 3\end{array}\right]=3\left(3\right)-\left(4\right)\left(-4\right)\\ =9+16\\ =25\end{array}$

Thus, the 2x2 matrix when the determinant is 25 is $\left[\begin{array}{cc}3& 4\\ -4& 3\end{array}\right]$ .

(c)

To determine

The 2x2 matrix when the determinant is -32.

Answer to Problem 60HP

The 2x2 matrix when the determinant is -32 is $\left[\begin{array}{cc}-2& -6\\ -6& -2\end{array}\right]$ .

Explanation of Solution

Given, The determinant is -32.

Calculation:

Calculate the matrix.

  $\begin{array}{c}\left[\begin{array}{cc}-2& -6\\ -6& -2\end{array}\right]=-2\left(-2\right)-\left(-6\right)\left(-6\right)\\ =4-36\\ =-32\end{array}$

Thus, the 2x2 matrix when the determinant is -32 is $\left[\begin{array}{cc}-2& -6\\ -6& -2\end{array}\right]$ .