Answer to Question #313387 in Linear Algebra for RAIN

Question

Find the inverse of matrix A given below using the formula A ^-1 =C^T/│A│

A=$\begin{vmatrix} -6 & -4 & -4 \\ -1 & -4 & 6 \\\ -6 & 5 & -1 \end{vmatrix}$

Answer 1

At first step we compute the determinant of $A$: $|A|=(-6)(-4)(-1)+(-1)(-4)5+(-4)(-6)6-(-6)\,6\,5+(-1)(-4)+6(-4)(-4)=-24+20+144+180+4+96=420$

Matrix $C^{\top}=\left(\begin{array}{lll}-26&-24&-40\\-37&-18&40\\-{29}&54&20\end{array}\right)$has the form: Matrix $A^{\top}$ has the form: $A=\left(\begin{array}{lll}-\frac{13}{210}&-\frac{2}{35}&-\frac{2}{21}\\-\frac{37}{420}&-\frac{3}{70}&\frac{2}{21}\\-\frac{29}{420}&\frac{9}{70}&\frac{1}{21}\end{array}\right)$.