Question

Suppose H is an ntimesn matrix. If the equation Hxequalsc is inconsistent for some c in set of real numbers R Superscript n​, what can you say about the equation Hxequals0​? ​Why?

Answer 1

The answer is explained below

Explanation:

Given that, the equation H*x = c is inconsistent for some c in R^n, we can say that the equation A*x = b has at least one solution for each b in R^n of IMT (Inverse Matrix Theorem) is not fulfilled.

Thanks to this we can say that by equivalence of theorem statement, the equation H*x = 0 will not have only the trivial solution. It will have non-trivial solutions too.