91Ó°ÊÓ

In Exercises 1-10, find the determinant of the given matrix. $$ \left[\begin{array}{lll} 6 & 2 & 1 \\ 0 & 4 & 1 \\ 0 & 0 & 5 \end{array}\right] $$

In Exercises 6-9, find the indicated determinant. \(\left|\begin{array}{rrr}1 & 4 & -2 \\ 3 & 13 & 0 \\ 2 & -1 & 3\end{array}\right|\)

Find the determinant of the given matrix. $$ \left[\begin{array}{rrrrr} 0 & 0 & 0 & 3 & 1 \\ 0 & 0 & 2 & 0 & -3 \\ 0 & -2 & 1 & 0 & 0 \\ 5 & -3 & 2 & 0 & 0 \\ -3 & 4 & 0 & 0 & 0 \end{array}\right] $$

In Exercises 6-9, find the indicated determinant. \(\left|\begin{array}{rrr}2 & -5 & 3 \\ 1 & 3 & 4 \\ -2 & 3 & 7\end{array}\right|\)

In Exercises 1-10, find the determinant of the given matrix. $$ \left[\begin{array}{rrrr} 2 & 3 & 4 & 6 \\ 2 & 0 & -9 & 6 \\ 4 & 1 & 0 & 2 \\ 0 & 1 & -i & 0 \end{array}\right] $$

Find the volume of the \(n \cdot b o x\) determined by the given vectors in \(R^{n}\). $$ [1,3,-5],[2,4,-1],[3,1,2] \text { in } \mathbb{R}^{3} $$

Find the determinant of the given matrix. $$ \left[\begin{array}{rrrr} 2 & -1 & 0 & 0 \\ 4 & 5 & 0 & 0 \\ 0 & 0 & 3 & 6 \\ 0 & 0 & -4 & 2 \end{array}\right] $$

In Exercises 1-10, find the determinant of the given matrix. $$ \left[\begin{array}{rrrr} 2 & 0 & -1 & 7 \\ 6 & 1 & 0 & 4 \\ 8 & -2 & 1 & 0 \\ 4 & 1 & 0 & 2 \end{array}\right] $$

In Exercises 6-9, find the indicated determinant. \(\left|\begin{array}{rrr}1 & -2 & 7 \\ 0 & 1 & 4 \\ 1 & 0 & 3\end{array}\right|\)

Find the volume of the \(n \cdot b o x\) determined by the given vectors in \(R^{n}\). $$ \begin{aligned} &{[1,0,0,1],[2,-1,3,0],[0,1,3,4]} \\ &{[-1,1,-2,1] \text { in } \mathbb{R}^{4}} \end{aligned} $$