73.9k views
2 votes
Find the? inverse, if it? exists, for the given matrix.

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

2 Answers

7 votes

Answer:

Explanation:

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

Find the? inverse, if it? exists, for the given matrix. @MATX{{3;3;-1};{-12;-12;4};{2;6;0}}-example-1
User Coldfused
by
8.0k points
4 votes

Answer:

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.

User Miriam Farber
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.