Question

Find the? inverse, if it? exists, for the given matrix.

@MATX{{3;3;-1};{-12;-12;4};{2;6;0}}

Answer 1

Explanation:

The Inverse of the matrix doesn't exist because the determinant is equal to 0.

Answer 2

The inverse of given matrix is not exist, since determinant is 0.

Explanation:

The inverse of a square matrix
`A` is
`A^(-1)` such that

`A A^(-1)=I` where I is the identity matrix.

Consider,
`A = \left[\begin{array}{ccc}3&3&-1\\-12&-12&4\\2&6&0\end{array}\right]`

`\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}`

`\det \begin{pmatrix}3&3&-1\\ -12&-12&4\\ 2&6&0\end{pmatrix}\\e 0`

`\det \begin{pmatrix}3&3&-1\\ -12&-12&4\\ 2&6&0\end{pmatrix}`

`\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \:`

`\det \begin{pmatrix}a&b&c\\ d&e&f\\ g&h&i\end{pmatrix}=a\cdot \det \begin{pmatrix}e&f\\ h&i\end{pmatrix}-b\cdot \det \begin{pmatrix}d&f\\ g&i\end{pmatrix}+c\cdot \det \begin{pmatrix}d&e\\ g&h\end{pmatrix}`

`=3\cdot \det \begin{pmatrix}-12&4\\ 6&0\end{pmatrix}-3\cdot \det \begin{pmatrix}-12&4\\ 2&0\end{pmatrix}-1\cdot \det \begin{pmatrix}-12&-12\\ 2&6\end{pmatrix}`

`=3\left(-24\right)-3\left(-8\right)-1\cdot \left(-48\right)`

`3\left(-24\right)-3\left(-8\right)-1\cdot \left(-48\right)=0`

Therefore, the inverse of given matrix is not exist, since determinant is 0.