Mathematics II20795 marksNumerical: determinant evaluationIntroduction
Evaluate the determinant of the matrix
Evaluate the determinant of the matrix $$\begin{bmatrix} 5 & -7 & 2 & 2 \ 0 & 3 & 0 & -4 \ -5 & -8 & 0 & 3 \ 0 & 5 & 0 & -6 \end{bmatrix}$$ [5]
$$A = \begin{bmatrix} 5 & -7 & 2 & 2 \ 0 & 3 & 0 & -4 \ -5 & -8 & 0 & 3 \ 0 & 5 & 0 & -6 \end{bmatrix}$$ Column 3 entries: $a{13}=2,\ a{23}=0,\ a{33}=0,\ a{43}=0$. Only one non-zero term: $$\det(A) = a{13}\cdot(-1)^{1+3}\cdot M{13} = 2\cdot M{13}$$ Delete row 1 and column 3: $$M{13} = \begin{v...