7 Bonus 5 pts Assume that A is n x n matrix If the equation

7. Bonus (5 pts) Assume that A is n x n matrix. If the equation Ax = b is inconsistent for some b in R^n, what can you say about the equation Ax = 0? Why?

Solution

If the equation Ax=b is inconsistent for some b, then the transformation x Ax is not one-to-one

It will have a nontrivial solution because , that means it may have no solution that it contradicts with \"The equation Ax=0 has only the trivial solution\" so it is true if both of them is false.