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8. Let T R2 R³ be a linear transformation such that T(1,2) T(-1,3)= (1,4, 2). Find T(x, y) and T-¹(x, y) if possible. = (0,3,-1) and

8. Let T R2 R³ be a linear transformation such that T(1,2) T(-1,3)= (1,4, 2). Find T(x, y) and T-¹(x, y) if possible. = (0,3,-1) and

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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7. Let V and W be finite-dimensional vector spaces and T: VW is an isomorphism. Prove that if 3 = {₁,.., Un} is a basis for V, then y = (T(₁) T(vn)} is a basis for W. 8. Let T R² R3 be a linear transformation such th that T(1,2) T(-1,3)= (1,4,2). Find T(x, y) and 7-1(x, y) if possible. = (0,3,-1) and
Transcribed Image Text:7. Let V and W be finite-dimensional vector spaces and T: VW is an isomorphism. Prove that if 3 = {₁,.., Un} is a basis for V, then y = (T(₁) T(vn)} is a basis for W. 8. Let T R² R3 be a linear transformation such th that T(1,2) T(-1,3)= (1,4,2). Find T(x, y) and 7-1(x, y) if possible. = (0,3,-1) and
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