Question

The equation ax = o has only the trivial solution if and only if the equation ax = b has a unique solution for every n x 1 column matrix b.

a. True
b. False

Answer 1

TRUE. The equation ax = 0 has only the trivial solution if and only if the equation ax = b has a unique solution for every n x 1 column matrix b.

Step-by-step explanation:

In order to determine whether the equation ax = 0 has only the trivial solution, we need to consider the equation ax = b. If the equation ax = b has a unique solution for every n x 1 column matrix b, then the equation ax = 0 will also have only the trivial solution. This is because if there is a unique solution for every b, then there is no other non-zero value of b that will satisfy the equation ax = 0.

Therefore, the statement is true.