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6. State two ways to determine whether or not an n x n matrix A is invertible.

6. State two ways to determine whether or not an n x n matrix A is invertible.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.4: Transistion Matrices And Similarity
Problem 29E
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6. State two ways to determine whether or not an n x n matrix A is invertible.
Transcribed Image Text:6. State two ways to determine whether or not an n x n matrix A is invertible.
Theorem 1 Let A = (ad). ! Example: Solve If ad-bc0, then A is invertible and A-¹ = ad-be (dd). a If ad bc = 0, then A is not invertible. Definition: The quantity ad-bc is the determinant of A, denoted by det A. (²7₂2)x= (²) X= for x using inverses.
Transcribed Image Text:Theorem 1 Let A = (ad). ! Example: Solve If ad-bc0, then A is invertible and A-¹ = ad-be (dd). a If ad bc = 0, then A is not invertible. Definition: The quantity ad-bc is the determinant of A, denoted by det A. (²7₂2)x= (²) X= for x using inverses.
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