Question

Consider matrix A.

A=[1 1
[1 1
(2 by 2 box)

Does the inverse of matrix A exist?

1The inverse of a square matrix exists only when
a. all entries are the same sign
b. no two entries are equal
c. the determinate does not equal zero
2The inverse of matrix A
a.does not exist
b. does exist

Answer 1

The determinate does not equal zero and does not exist

Explanation:

Answer 2

1. Inverse of matrix A exist If and Only If

c. the determinate does not equal zero

2. The inverse of matrix A

a.does not exist

Explanation:

Given:

Consider matrix A. 2 by 2

A=
`\left[\begin{array}{cc}1&1\\1&1\end{array}\right]`

To Find:

Does the inverse of matrix A exist?

Solution:

1. Inverse of matrix A exist If and Only If

c. the determinate does not equal zero

For the Given Matrix A We have

Det |A| = 1×1 -1×1

Det |A| = 0

2. The inverse of matrix A

a.does not exist