Question

Suppose A is an n × n invertible matrix. Which of the following statements is/are true?

A. The homogeneous system Ax = 0 has no solution.

B. The nonhomogeneous system Ax = b has a unique solution for each non-zero n × 1 vector b.


1. Only A 2. Only B 3. Both A and B 4. Neither A nor B

Answer 1

Well since A is invertible, \(Ax=\mathbf{0} \Leftrightarrow x=A^{-1}\mathbf{0}=\mathbf{0}\). So there is always that solution (which is unique as well). So you know A is false. Can you figure out B?

Answer 2

can a nonhomogeneous system be inverted?

Answer 3

I think B is true, well that how i answered. was i right?

Answer 4

All you need is that the matrix has a unique inverse, which is true. So you are right

Answer 5

Thanx