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Let B = {v1, v2, V3, V4} be a basis for R4. Let T:R4 → R* be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are: T(v1) = 2v1 -2v2 +2v3 +3v4 +3v3 T(v2) = 6v1 T(v3) = T(v4) = %3D V1 -V2 +V4 Vị +2v2 +v3 -2v4

Let B = {v1, v2, V3, V4} be a basis for R4. Let T:R4 → R* be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are: T(v1) = 2v1 -2v2 +2v3 +3v4 +3v3 T(v2) = 6v1 T(v3) = T(v4) = %3D V1 -V2 +V4 Vị +2v2 +v3 -2v4

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(a) Find the matrix for T with respect to the basis B: [T]B =? (b) Let x = c1Vi + C2V2 + C3v3 + C4V4, where c1, c2, C3, C4 E R. What is [x]B : What is [T(x)]B = CB(T(x)) =? Св(x) —?
Transcribed Image Text:(a) Find the matrix for T with respect to the basis B: [T]B =? (b) Let x = c1Vi + C2V2 + C3v3 + C4V4, where c1, c2, C3, C4 E R. What is [x]B : What is [T(x)]B = CB(T(x)) =? Св(x) —?
Let B = {v1, V2, V3, V4} be a basis for R4. Let T: R4 -→ R* be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are: +3v4 T(v1) = 2v1 -2v2 T(v2) T(v3) T(v4) = +2v3 +3v3 6v1 V1 -V2 +V4 Vị +2v2 +v3 -2v4
Transcribed Image Text:Let B = {v1, V2, V3, V4} be a basis for R4. Let T: R4 -→ R* be the linear transformation such that on the basis vectors v1, V2, V3, V4, its values are: +3v4 T(v1) = 2v1 -2v2 T(v2) T(v3) T(v4) = +2v3 +3v3 6v1 V1 -V2 +V4 Vị +2v2 +v3 -2v4
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