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Section 4.3 Determinant Fundamentals: Homework
Exercises Exercises
Exercise Group.
Find the determinant of each of the following matrices.
1.
\(A=\left(\begin{array}{rr}4\amp 3\\ -2\amp 5 \end{array} \right)\)
2.
\(A=\left(\begin{array}{rr}6\amp 8\\ 15\amp 20 \end{array} \right)\)
3.
\(A=\left(\begin{array}{rr}-2\amp 7\\ 8\amp 3 \end{array} \right)\)
4.
\(A=\left(\begin{array}{rr} 6\amp -1\\ -2\amp 3 \end{array} \right)\)
Exercise Group.
Find the determinant of each of the following matrices.
5.
\(A=\left(\begin{array}{rrr}5\amp 1\amp -2\\-7\amp 2\amp -4\\3\amp 0\amp -6 \end{array} \right)\)
6.
\(A = \left(\begin{array}{rrr} 5 \amp 1 \amp -2 \\ 1 \amp 3 \amp -2\\ 0 \amp 4 \amp -1 \end{array} \right)\)
7.
\(A\,=\,\left(\begin{array}{r}7\\-3\\1 \end{array} \right)\left(\begin{array}{rrr}2\amp 6\amp -3 \end{array} \right)\text{.}\)
8.
\(A\,=\,\left(\begin{array}{r}9\\-2\\5 \end{array} \right)\left(\begin{array}{rrr}0\amp 7\amp -1 \end{array} \right)\text{.}\)
Exercise Group.
Find the determinant of each of the following matrices.
9.
\(B=\left(\begin{array}{rrrr}1\amp 4\amp 0\amp -3\\-3\amp 5\amp 1\amp 7\\6\amp -4\amp -5\amp 9\\2\amp 1\amp 1\amp -1 \end{array} \right)\)
10.
\(A = \left(\begin{array}{rrrr} -2 \amp 3 \amp 1 \amp -2 \\ 1 \amp 4 \amp 0 \amp 1\\ 2 \amp 1 \amp 0 \amp -2 \\ 3 \amp 1 \amp -2 \amp 4 \end{array} \right)\)
11.
Suppose \(A\in\R^{5\times 5}\) has \(\det(A)=2\text{.}\) Compute (be sure to cite a theorem, definition or property to justify each calculation)
\(\displaystyle \det(3A)\)
\(\displaystyle \det(-A)\)
12.
T/F: \(\,\,\det(A-B)=\det(A)-\det(B)\text{.}\) Give a reason if true or a counterexample if false.
