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(a) Define: invertible linear transformation. (b) T: (21,72) → (6x₁ − 8x2, −5x₁ +72) is a linear transformation from R² to R². Show that T is invertible and find a formula for T¹ alike to the one for T. Also, state the matrix representations for T and T-¹ in the standard bases.

(a) Define: invertible linear transformation. (b) T: (21,72) → (6x₁ − 8x2, −5x₁ +72) is a linear transformation from R² to R². Show that T is invertible and find a formula for T¹ alike to the one for T. Also, state the matrix representations for T and T-¹ in the standard bases.

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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1. (a) Define: invertible linear transformation. (b) T: (1,2) → (6x₁ − 8x2, −5x₁ +7x2) is a linear transformation from R2 to R². Show that T is invertible and find a formula for T-¹ alike to the one for T. Also, state the matrix representations for T and T-¹ in the standard bases.
Transcribed Image Text:1. (a) Define: invertible linear transformation. (b) T: (1,2) → (6x₁ − 8x2, −5x₁ +7x2) is a linear transformation from R2 to R². Show that T is invertible and find a formula for T-¹ alike to the one for T. Also, state the matrix representations for T and T-¹ in the standard bases.
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