Mathematics II20805 marksNumerical: determinant evaluationProperties
Evaluate the determinant of the matrix.
Evaluate the determinant of the matrix.
$$\begin{bmatrix} 1 & -7 & 8 & 9 & -6 \ 0 & 2 & -5 & 7 & 3 \ 0 & 0 & 2 & 4 & -1 \ 0 & 0 & 1 & 5 & 0 \ 0 & 0 & 0 & -1 & 0 \end{bmatrix}$$
[5]
$$A = \begin{bmatrix} 1 & -7 & 8 & 9 & -6 \ 0 & 2 & -5 & 7 & 3 \ 0 & 0 & 2 & 4 & -1 \ 0 & 0 & 1 & 5 & 0 \ 0 & 0 & 0 & -1 & 0 \end{bmatrix}$$ Note: The matrix is not fully upper triangular because $a{43} = 1 \neq 0$. So cofactor expansion is required. --- Only $a{11} = 1$ is nonzero: $$\det(A)...