Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to I_n. By Theorem 7, this shows that A must
be invertible. 

Data from in Theorem 7

Transcribed Image Text:

Cramer's Rule Let A be an invertible n × n matrix. For any b in R", the unique solution x of Ax = b has entries given by X₁ = det A; (b) det A i=1,2,..., n (1)