The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T¯1. T(x1 x2)=(5x18x2,-5x1 +9x2) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is 5. (Simplify your answer.) T-1 9 8 5X1+5X2+1X3+1X4 (Type an ordered pair. Type an expression using x₁ and x2 as the variables.)
The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T¯1. T(x1 x2)=(5x18x2,-5x1 +9x2) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is 5. (Simplify your answer.) T-1 9 8 5X1+5X2+1X3+1X4 (Type an ordered pair. Type an expression using x₁ and x2 as the variables.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Determinants
Section3.1: The Determinants Of A Matrix
Problem 70E: The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six...
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