A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an
inverse.
-$$\left[ \begin{array} { l l l }
1 & 2 & 3 \
2 & 0 & 5 \
1 & 2 & 3
\end{array} \right]$$
A) Yes
B) No

Question

A matrix has an inverse if and only if its determinant does not equal 0. Determine whether the given matrix has an
inverse.
-$$\left[ \begin{array} { l l l } 
1 & 2 & 3 \
2 & 0 & 5 \
1 & 2 & 3
\end{array} \right]$$
A) Yes
B) No

Quizplus · Accepted Answer

The matrix does not have an inverse because two of its rows are identical (the first and the third rows), which makes its determinant equal to 0. A matrix with a determinant of 0 is singular and does not have an inverse.

A Matrix Has an Inverse If and Only If Its [123205123]\left[ \begin{array} { l l l } 1 & 2 & 3 \\2 & 0 & 5 \\1 & 2 & 3\end{array} \right]​121​202​353​​

A Matrix Has an Inverse If and Only If Its $\left[ \begin{array} { l l l } 1 & 2 & 3 \\2 & 0 & 5 \\1 & 2 & 3\end{array} \right]$