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1. (a) Define: invertible linear transformation. (b) T: (7₁,72) → (67₁ - 872,-57₁ +77₂) is a linear transformation from R² to R². Show that T is invertible and find a formula for Talike to the one for T. Also, state the matrix representations for T and T-¹ in the standard bases. 2. If a linear transformation T from R" to R is invertible, show that n = m.

1. (a) Define: invertible linear transformation. (b) T: (7₁,72) → (67₁ - 872,-57₁ +77₂) is a linear transformation from R² to R². Show that T is invertible and find a formula for Talike to the one for T. Also, state the matrix representations for T and T-¹ in the standard bases. 2. If a linear transformation T from R" to R is invertible, show that n = m.

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: (2₁,22) → (6x₁ − 8x2,−571 +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. 2. If a linear transformation T from R" to R" is invertible, show that n = m.
Transcribed Image Text:1. (a) Define: invertible linear transformation. (b) T: (2₁,22) → (6x₁ − 8x2,−571 +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. 2. If a linear transformation T from R" to R" is invertible, show that n = m.
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