Suppose A is n x n and the equation Ax = 0 has only the trivial solution.
Question:
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 In. 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)
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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