Numerical Methods & Linear Algebra

Math 2890-003

(1 point) Let \[A=\left(\begin{array}{rrrrrr} -8 & 0 & 0 & 0 & 0 & 0 \\ -9 & 6 & 0 & 0 & 0 & 0 \\ 7 & -2 & 1 & 0 & 0 & 0 \\ -5 & -2 & 5 & -4 & 0 & 0 \\ 0 & 2 & 2 & -1 & 1 & 0 \\ 9 & 9 & 2 & 8 & -1 & 2 \end{array}\right).\] Find the determinant of $A$ if it exists. Show and explain your computations. If the determinant doesn't exist, explain why it doesn't.

(1 point) Let \[A=\left(\begin{array}{rrrrrrrr} 3 & 5 & 6 & 4 & 0 & 1 & 0 & 4 \\ 1 & 1 & 7 & 2 & 0 & 6 & 5 & 0 \\ 0 & 0 & 9 & 2 & 4 & 1 & 2 & 3 \\ 0 & 0 & 3 & 7 & 4 & 6 & 7 & 2 \\ 0 & 0 & 0 & 0 & 0 & 8 & 9 & 4 \\ 0 & 0 & 0 & 0 & 5 & 9 & 3 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 9 & 7 \\ 0 & 0 & 0 & 0 & 0 & 0 & 3 & 8 \end{array}\right).\] Find the determinant of $A$ if it exists. Show and explain your computations. If the determinant doesn't exist, explain why it doesn't.

(1 point) Let \[A=\left(\begin{array}{rrrr} 2 & 8 & 1 & 0 \\ 1 & 8 & 3 & 3 \\ 3 & 6 & 1 & 1 \end{array}\right).\] Find the determinant of $A$ if it exists. Show and explain your computations. If the determinant doesn't exist, explain why it doesn't.

(1 point) Let \[A=\left(\begin{array}{rrrrr} -4 & 0 & 0 & 0 & 0 \\ 4 & -1 & 0 & 0 & 0 \\ -4 & 4 & 2 & 0 & 0 \\ -3 & 5 & -3 & -1 & 0 \\ -3 & -1 & 0 & -5 & -3 \end{array}\right)\left(\begin{array}{rrrrr} 4 & -5 & -2 & 1 & 2 \\ 0 & -2 & -3 & -5 & 2 \\ 0 & 0 & -1 & 5 & 1 \\ 0 & 0 & 0 & 5 & -4 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right).\] Find the determinant of $A$ if it exists. Show and explain your computations. If the determinant doesn't exist, explain why it doesn't.

(1 point) Let \[A=\left(\begin{array}{rrrr} 5 & 5 & 3 & 9 \\ 1 & 8 & 0 & 2 \\ 3 & 6 & 3 & 5 \\ 1 & 9 & 0 & 3 \end{array}\right).\] Find the determinant of $A$ if it exists. Show and explain your computations. If the determinant doesn't exist, explain why it doesn't.