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Q1. Given B = {v1 = (0, 1, 1, 1), v2 = (2, 1, –1, –1), v3 = (1,4, –1,2), v4 = (6,9, 4, 2)} B' = {wi = (0,8, 8), wz = (-7,8, 1), wz = (-6,9, 1)} з -2 1 0 A = 1 6 2 1 -3 0 7 1 and T : R' – R such that matrix A is the transformation matrix in relation to B and B' basis. --() a)Find a formula for T(1,82, 13, 74) - and use that formula to get T(2,2,0,0). b)find Im(T) · and a basis for Im(T\What is the dim(Im(T}}? - c) find Ker(T) and a basis for Ker(T). What is the dim(Ker(T)}?

Q1. Given B = {v1 = (0, 1, 1, 1), v2 = (2, 1, –1, –1), v3 = (1,4, –1,2), v4 = (6,9, 4, 2)} B' = {wi = (0,8, 8), wz = (-7,8, 1), wz = (-6,9, 1)} з -2 1 0 A = 1 6 2 1 -3 0 7 1 and T : R' – R such that matrix A is the transformation matrix in relation to B and B' basis. --() a)Find a formula for T(1,82, 13, 74) - and use that formula to get T(2,2,0,0). b)find Im(T) · and a basis for Im(T\What is the dim(Im(T}}? - c) find Ker(T) and a basis for Ker(T). What is the dim(Ker(T)}?

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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Q1. Given B = {vi = (0, 1, 1, 1), v2 = (2, 1, –1, –1), v3 = (1, 4, –1,2), v4 = (6,9, 4, 2)} %3D B' = {wi = (0, 8, 8), wz = (-7,8, 1), wz = (-6,9, 1)} %3D %3D -2 1 0 1 6 2 1 -3 0 7 1 and T : R' → R such that matrix A is the transformation matrix in relation to B and B' basis. A = a)Find a formula for T(x1,#2, X3, X4) . and use that formula to get T(2,2,0, 0). b)find Im(T) and a basis for Im(T\What is the dim(Im(T}}? .c) find Ker(T) and a basis for Ker(T). What is the dim(Ker(T))?
Transcribed Image Text:Q1. Given B = {vi = (0, 1, 1, 1), v2 = (2, 1, –1, –1), v3 = (1, 4, –1,2), v4 = (6,9, 4, 2)} %3D B' = {wi = (0, 8, 8), wz = (-7,8, 1), wz = (-6,9, 1)} %3D %3D -2 1 0 1 6 2 1 -3 0 7 1 and T : R' → R such that matrix A is the transformation matrix in relation to B and B' basis. A = a)Find a formula for T(x1,#2, X3, X4) . and use that formula to get T(2,2,0, 0). b)find Im(T) and a basis for Im(T\What is the dim(Im(T}}? .c) find Ker(T) and a basis for Ker(T). What is the dim(Ker(T))?
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