Chapter 11.4, Problem 6AYU

To determine

To fill: The blank in the statement “If a matrix A has no inverse, it is called _____ matrix”.

Answer to Problem 6AYU

The complete statement is “If a matrix A has no inverse, it is called singular matrix.”

Explanation of Solution

Given information:

The statement “If a matrix A has no inverse, it is called _____ matrix”.

Consider the provided statement “If a matrix A has no inverse, it is called _____ matrix”.

In a matrix elements written horizontal form a part of row and elements written in the vertical form a part of column.

For example: $\left(\begin{array}{cc}1& 3\\ 4& 12\end{array}\right)$

For a matrix A , the inverse of a $2\times 2$ is given by the formula $A{A}^{-1}=I_2$ , where $I_2$ is the identity matrix, we use the Gauss-Jordan elimination to find the inverse.

  $2\times 2$ .

Since, the determinant of above matrix is 0 because $12-12=0$ . When inverse is evaluated it is divided by the determinant so if determinant is 0 the inverse cannot be evaluated.

Matrices whose inverse cannot be evaluated are singular matrices otherwise non singular matrices.

Thus, the complete statement is “If a matrix A has no inverse, it is called singular matrix”.