Suppose A is an n x n matrix with the property that the equation Ax = b has at least one solution for each b in Rⁿ.
Without using Theorems 5 or 8, explain why each equation
Ax = b has in fact exactly one solution.

Data from in Theorem 5

Data from in Theorem 8

Transcribed Image Text:

If A is an invertible n × n matrix, then for each b in R", the equation Ax = b has the unique solution x = A-¹b.