Question

The inverse of the matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 3& 4\end{array}\right]$

• A. is $\left[\begin{array}{ccc}1& 5& 2\\ 3& 1& -2\\ 1& 2& 3\end{array}\right]$
• B. is $\left[\begin{array}{ccc}1& 2& 3\\ 1& 5& 9\\ 3& 7& 2\end{array}\right]$
• C. is $\left[\begin{array}{ccc}7& 9& 1\\ 3& 5& 7\\ 2& 1& 3\end{array}\right]$
• D. does not exist.

Answer 1

The correct option is D does not exist.

Give matrix is,

$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 3& 4\end{array}\right]$

Lets first find the determinant to use in the equation:

$A^{-1}=\frac{1}{|A|}.Adj\left(A\right).$

If $|A|=0$ we can rightaway say that the inverse doesn’t exist.

So, $|A|=1\times 1-2\times 2+3\times 1$

$=1-4+3$

$=0$

This shows that the given matrix is non-invertible or singular.

Hence, the inverse doesn’t exist.