Question

Give examples of matrices A and B such that

A+B is not invertible, although A and B are invertible.

Answer 1

An example of matrices A and B such that A + B is not invertible, although A and B are invertible.

Step-by-step explanation:

To find an example of matrices A and B such that A + B is not invertible, although A and B are invertible, we can consider the following:

Let A = [1 0] and B = [0 1].

A and B are both invertible because they are non-singular matrices (their determinants are non-zero). However, when we add them together, A + B = [1 0] + [0 1] = [1 1].

The matrix [1 1] is singular because its determinant is zero. Therefore, A + B is not invertible, although A and B are invertible.