Chapter 8.3, Problem 3E

To determine

Tofind:If the matrix A has an inverse it is called invertible or _____if it does not have an inverse then it’s called _______

Answer to Problem 3E

If a matrix A has an inverse, it is called invertible or non-singular, if it does not have an inverse, it’s called singular.

Explanation of Solution

Given:A matrix has an inverse

A matrix doesn’t have an inverse

Concept used:

Finding out the inverse of a matrix, its required to find the quotient of the adjoint of the matrix and its determinant.

Calculation:

If a matrix A has an inverse, it is called invertible or non-singular, if it does not have an inverse, it’s called singular.

A singular matrix can be also described as the one who discriminant is equals to 0.

While finding out the inverse of a matrix, its required to find the quotient of the adjoint of the matrix and its determinant.

Hence, it’s crucial that the determinant is finite and non- zero.

Hence if the determinant is 0, then the inverse cannot exist.