Exam 50: The Determinant of a Square Matrix

Find the determinant of the matrix.Expand by cofactors on the row or column that appears to make the computations easiest.​ $\left[ \begin{array} { c c c } 9 & 8 & - 2 \\2 & 2 & 0 \\- 9 & 8 & 2\end{array} \right]$ ​

Find the determinant of the matrix by the method of expansion by cofactors.Expand using the row 1.​ $\left[ \begin{array} { c c c } - 3 & 2 & 1 \\4 & 5 & 6 \\2 & - 3 & 1\end{array} \right]$ ​

Find all the cofactors of the matrix.​ $\left[ \begin{array} { c c c } - 4 & 0 & 2 \\4 & 4 & 3 \\3 & - 3 & 3\end{array} \right]$ ​

Evaluate the determinant in which the entries are functions.​ $\left| \begin{array} { c c } 2 u & - 4 \\- 4 & 3 v\end{array} \right|$ ​

Find the determinant of the matrix.​ $\left[ \begin{array} { c c } 2 & - 2 \\8 & - 16\end{array} \right]$ ​

Find the determinant of the matrix.​ $\left[ \begin{array} { c c } 2 & - 5 \\0 & 0\end{array} \right]$ ​

​Find the determinant of the matrix $\left[ \begin{array} { c } - \frac { 1 } { 6 } - \frac { 1 } { 6 } \\\\- 1 - \frac { 2 } { 5 }\end{array} \right]$ . ​

Find all the cofactors of the matrix.​ $\left[ \begin{array} { c c } 0 & 6 \\3 & - 6\end{array} \right]$ ​

Given $A = \left[ \begin{array} { c c c } 0 & 2 & 4 \\- 6 & - 4 & 2 \\0 & 8 & 2\end{array} \right]$ ,find $| A |$ .

Find all minors of the matrix.​ $\left[ \begin{array} { c c } 0 & 8 \\4 & - 8\end{array} \right]$ ​

Solve for x given the following equation involving a determinant. $\left| \begin{array} { c c } x + 2 & 5 \\- 1 & x + 8\end{array} \right| = 0$

Use the matrix capabilities of a graphing utility to evaluate the determinant.​ $\left[ \begin{array} { c c c } 3 & 1 & - 6 \\0 & - 6 & 9 \\1 & 1 & 1\end{array} \right]$ ​

Use the matrix capabilities of a graphing utility to find the determinant of the matrix $\left[ \begin{array} { c c c } 0.2 & - 0.6 & 0.6 \\0.8 & 0.4 & 0 \\- 0.4 & - 1.4 & 1.0\end{array} \right]$ .

Use the matrix capabilities of a graphing utility to find the determinant of the matrix $\left[ \begin{array} { c c c } 16 & 24 & 8 \\0 & 40 & - 16 \\0 & 0 & - 16\end{array} \right]$ .

Find $A B$ .​ $A = \left[ \begin{array} { c c } - 2 & 0 \\0 & 4\end{array} \right] , B = \left[ \begin{array} { c c } 3 & 0 \\0 & - 2\end{array} \right]$ ​

Evaluate the determinant.​ $\left| \begin{array} { l l l } 2 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 6\end{array} \right|$ ​

Find the determinant of the matrix by the method of expansion by cofactors.Expand using the column 2.​ $\left[ \begin{array} { c c c } - 3 & 2 & 1 \\4 & 5 & 6 \\2 & - 3 & 1\end{array} \right]$ ​

Find all the cofactors of the matrix.​ $\left[ \begin{array} { c c } 6 & 7 \\4 & - 8\end{array} \right]$ ​

Find all minors of the matrix.​ $\left[ \begin{array} { c c } 4 & 5 \\4 & - 8\end{array} \right]$ ​

Find the determinant of the matrix $\left[ \begin{array} { l l } - 1 & 2 \\- 6 & 4\end{array} \right]$ .