T(x1.x2) = (3x1 - 8x2,- 3x1 + 7x2) 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.)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
icon
Related questions
Question

HOMEWORK 11 QUESTION 6

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) = (3x₁ - 8x2, -3x₁ + 7x₂)
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.)
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) = (3x₁ - 8x2, -3x₁ + 7x₂) 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.)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage