Question #313387

Find the inverse of matrix A given below using the formula A -1 =CT/│A│

A=644146 651\begin{vmatrix} -6 & -4 & -4 \\ -1 & -4 & 6 \\\ -6 & 5 & -1 \end{vmatrix}


1
Expert's answer
2022-03-19T02:39:34-0400

At first step we compute the determinant of AA: A=(6)(4)(1)+(1)(4)5+(4)(6)6(6)65+(1)(4)+6(4)(4)=24+20+144+180+4+96=420|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=(262440371840295420)C^{\top}=\left(\begin{array}{lll}-26&-24&-40\\-37&-18&40\\-{29}&54&20\end{array}\right)has the form: Matrix AA^{\top} has the form: A=(132102352213742037022129420970121)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).


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