The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T¹ T(x1.x2) = (2x1-6x2,- 2x₁ +5x2) 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.) T¹(x₁-x₂) = (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 T¹ T(x1.x2) = (2x1-6x2,- 2x₁ +5x2) 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.) T¹(x₁-x₂) = (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...
Related questions
Question
Transcribed Image Text:The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T¹
T(x1.x2) = (2x1-6x2,- 2x₁ +5x2)
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.)
T¹(x₁,x₂) =
(Type an ordered pair. Type an expression using X₁ and x₂ as the variables.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
