6. Prove the formulas for calculating the inverse of a small matrix: a. Gauss-Jordan formulas for the inverse of an invertible 2 × 2 or 3 x 3 matrix b. The triple-product formula for the inverse of an invertible 3 × 3 matrix c. The Cayley-Hamilton formulas for the inverse of an invertible 3 × 3 or 4 x 4 matrix

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 13E
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6. Prove the formulas for calculating the inverse of a small matrix:
a. Gauss-Jordan formulas for the inverse of an invertible 2 × 2 or 3 x 3 matrix
b. The triple-product formula for the inverse of an invertible 3 × 3 matrix
c. The Cayley-Hamilton formulas for the inverse of an invertible 3 × 3 or 4 x 4
matrix
Transcribed Image Text:6. Prove the formulas for calculating the inverse of a small matrix: a. Gauss-Jordan formulas for the inverse of an invertible 2 × 2 or 3 x 3 matrix b. The triple-product formula for the inverse of an invertible 3 × 3 matrix c. The Cayley-Hamilton formulas for the inverse of an invertible 3 × 3 or 4 x 4 matrix
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