Question

Which of the following matrices will not have an inverse?

(a) \(\begin{bmatrix}2&4\\-1&1\end{bmatrix}\)

(b) \(\begin{bmatrix}1&5&2\\6&4&2\\1&3&2\end{bmatrix}\)

(c) \(\begin{bmatrix}1&2\\1&1\end{bmatrix}\)

(d) \(\begin{bmatrix}1&2&5\\3&6&4\end{bmatrix}\)

This question was posed to me in class test.

Enquiry is from Invertible Matrices topic in portion Matrices of Mathematics – Class 12

Answer 1

Correct option is (d) \(\begin{bmatrix}1&2&5\\3&6&4\end{bmatrix}\)

The explanation: The matrix A=\(\begin{bmatrix}1&2&5\\3&6&4\end{bmatrix}\) will not have an inverse as it is a rectangular matrix. Rectangular matrix does not possess an inverse matrix.