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) = (5x₁9x2,- 5x₁ + 6x₂) 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.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 T¹
T(X1X2) = (5x₁9x2,- 5x₁ +6x₂)
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(X1X2) = (5x₁9x2,- 5x₁ +6x₂) 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
Step 1

Introduction:

The linear transformation is invertible if and only if the corresponding matrix is invertible.

A matrix is invertible if its determinant is non zero.

Given:  Linear transformation. Tx1, x2=5x1-9x2, -5x1+6x2

To find:

T is invertible or not.

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