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.)

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter4: Systems Of Linear Equations
Section4.6: Solve Systems Of Equations Using Determinants
Problem 4.94TI: Evaluate the determinant |322214103| , by expanding by minors along the first row.
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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.)
Transcribed Image Text: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.)
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