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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) = (5x1-9x2, - 5x₁ +8x2) www 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.) T¹ (X₁, X2) = (Type an ordered pair. Type an expression using x, 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) = (5x1-9x2, - 5x₁ +8x2) www 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.) T¹ (X₁, X2) = (Type an ordered pair. Type an expression using x, and x2 as the variables.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) = (5x1-9x2,- 5x₁ + 8x2) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.) 5 T1 (Type an ordered pair. Type an expression using x₁ and x2 as the variables.) F1 K F2 A- F3 + F4 F5 * F6 F7 F8 F9
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) = (5x1-9x2,- 5x₁ + 8x2) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.) 5 T1 (Type an ordered pair. Type an expression using x₁ and x2 as the variables.) F1 K F2 A- F3 + F4 F5 * F6 F7 F8 F9
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