91Ó°ÊÓ

Use Theorem 3.2 .5 to determine whether the given matrix is invertible or not. $$\left[\begin{array}{rr} -1 & 1 \\ 1 & -1 \end{array}\right]$$

Evaluate the given determinant by using the Cofactor Expansion Theorem. Do not apply elementary row operations. $$\left|\begin{array}{rrr} -4 & 2 & -1 \\ 7 & -3 & 2 \\ -6 & 6 & 2 \end{array}\right|$$

Use Cramer's rule to determine the unique solution for \(x\) to the system \(A x=b\) for the given matrix \(A\) and vector \(\mathbf{b}\). $$A=\left[\begin{array}{rl}2 & 8 \\\\-2 & 4\end{array}\right], \mathbf{b}=\left[\begin{array}{r}0 \\\\-3\end{array}\right].$$

Use Cramer's rule to determine the unique solution for \(x\) to the system \(A x=b\) for the given matrix \(A\) and vector \(\mathbf{b}\). $$A=\left[\begin{array}{ll}3 & 5 \\\6 & 2\end{array}\right], \mathbf{b}=\left[\begin{array}{l}4 \\ 9\end{array}\right].$$

Evaluate the determinant of the given matrix. \(A=\left[\begin{array}{rr}0 & -2 \\ 5 & 1\end{array}\right]\).

Let $$A=\left[\begin{array}{rrr} 1 & 2 & -1 \\ 2 & 1 & 4 \end{array}\right], \quad B=\left[\begin{array}{rr} 2 & 1 \\ 5 & -2 \\ 4 & 7 \end{array}\right], \quad C=\left[\begin{array}{rrr} 1 & 0 & 5 \\ 3 & -1 & 4 \\ 2 & -2 & 6 \end{array}\right]$$. Compute the determinants, where possible. $$\operatorname{det}(B)$$

Use Theorem 3.2 .5 to determine whether the given matrix is invertible or not. $$\left[\begin{array}{ll} 2 & 1 \\ 3 & 2 \end{array}\right]$$

Evaluate the given determinant by using the Cofactor Expansion Theorem. Do not apply elementary row operations. $$\left|\begin{array}{ccc} 1 & 0 & -2 \\ 3 & 1 & -1 \\ 7 & 2 & 5 \end{array}\right|$$

Evaluate the determinant of the given matrix. \(A=\left[\begin{array}{rr}6 & -3 \\ -5 & -1\end{array}\right]\).

Let $$A=\left[\begin{array}{rrr} 1 & 2 & -1 \\ 2 & 1 & 4 \end{array}\right], \quad B=\left[\begin{array}{rr} 2 & 1 \\ 5 & -2 \\ 4 & 7 \end{array}\right], \quad C=\left[\begin{array}{rrr} 1 & 0 & 5 \\ 3 & -1 & 4 \\ 2 & -2 & 6 \end{array}\right]$$. Compute the determinants, where possible. $$\operatorname{det}(C)$$