91Ó°ÊÓ

Find the determinant of the matrix. $$[1]$$

Determine which property of determinants the equation illustrates. $$\left|\begin{array}{ll}2 & -6 \\\1 & -3\end{array}\right|=0$$

Find the adjoint of the matrix \(A .\) Then use the adjoint to find the inverse of \(A\) (if possible). $$A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right]$$

The Determinant of a Matrix Product In Exercises \(1-6,\) find \((a)|A|,\) (b) \(|B|,\) (c) \(A B,\) and \((d)|A B| .\) Then verify that \(|\boldsymbol{A}||\boldsymbol{B}|=|\boldsymbol{A B}|\). $$A=\left[\begin{array}{rr}-2 & 1 \\\4 & -2\end{array}\right], \quad B=\left[\begin{array}{rr}1 & 1 \\\0 & -1\end{array}\right]$$

Find the determinant of the matrix. $$[-3]$$

Determine which property of determinants the equation illustrates. $$\left|\begin{array}{rr}-4 & 5 \\\12 & -15\end{array}\right|=0$$

Find the adjoint of the matrix \(A .\) Then use the adjoint to find the inverse of \(A\) (if possible). $$A=\left[\begin{array}{rr} -1 & 0 \\ 0 & 4 \end{array}\right]$$

The Determinant of a Matrix Product In Exercises \(1-6,\) find \((a)|A|,\) (b) \(|B|,\) (c) \(A B,\) and \((d)|A B| .\) Then verify that \(|\boldsymbol{A}||\boldsymbol{B}|=|\boldsymbol{A B}|\). $$A=\left[\begin{array}{ll}3 & 4 \\\4 & 3\end{array}\right], \quad B=\left[\begin{array}{rr}2 & -1 \\\5 & 0\end{array}\right]$$

Find the determinant of the matrix. $$\left[\begin{array}{ll}2 & 1 \\ 3 & 4\end{array}\right]$$

Determine which property of determinants the equation illustrates. $$\left|\begin{array}{rrr}1 & 4 & 2 \\\0 & 0 & 0 \\\5 & 6 & -7\end{array}\right|=0$$