Chapter 4.8, Problem 54E

a

To determine

To Find: The determinant of diagonal matrix.

Answer to Problem 54E

Determinant of $A=15$

Explanation of Solution

Given information: Determinant $A=\left[\begin{array}{cc}3& -2\\ 0& 5\end{array}\right]$

Concept Used: If A is a square matrix, the determinant of A is the sum of the entries in any row of A multiplied by their respective cofactors

Calculation:

Determinant of A $=\left|A\right|=3\times 5-0=15$

b

To determine

To Find: The determinant of diagonal matrix

Answer to Problem 54E

Determinant of $B=-75$

Explanation of Solution

Given information: determinant $A=\left[\begin{array}{ccc}3& -7& 1\\ 0& -5& -9\\ 0& 0& 5\end{array}\right]$

Calculation:

If A is a square matrix, the determinant of A is the sum of the entries in any row of A multiplied by their respective cofactors

Determinant of B $=\left|B\right|=3\times \left(-25-0\right)+7\left(0-0\right)+1\left(0-0\right)=-75$

c.

To determine

To Find: The determinant of diagonal matrix

Answer to Problem 54E

Determinant of $C=-120$

Explanation of Solution

Given information: determinant $A=\left[\begin{array}{cccc}4& 0& 0& 0\\ 3& -3& 0& 0\\ 3& 6& 5& 0\\ 2& -2& 1& 2\end{array}\right]$

Concept Used: If A is a square matrix, the determinant of A is the sum of the entries in any row of A multiplied by their respective cofactors

Calculation:

Determinant of C $=\left|C\right|=4\times \left[\begin{array}{ccc}-3& 0& 0\\ 6& 5& 0\\ -2& 1& 2\end{array}\right]-0+0-0=4\times -3\times 10=-120$