Question

Find the? inverse, if it? exists, for the given matrix. @MATX{{3;3;-1};{-12;-12;4};{2;6;0}}

Answer 1

Answer:

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

Step-by-step explanation:

The inverse of a square matrix $A$ is $A^{-1}$ such that

$A A^{-1}=I$ where I is the identity matrix.

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

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

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

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

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

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

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

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

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

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

Answer 2

Answer:

Step-by-step explanation:

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