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Let S = {1, 2, 3} be the standard basis for R³, and let B = {₁, 2, 3} be the basis that results when the linear transformation defined by T(#₁, #2, #3) = (₁ + x2, 2x1 − x₂ + 4x3, x2 + 3x3) is applied to each vector in S. Find the transition matrix PBS.

Let S = {1, 2, 3} be the standard basis for R³, and let B = {₁, 2, 3} be the basis that results when the linear transformation defined by T(#₁, #2, #3) = (₁ + x2, 2x1 − x₂ + 4x3, x2 + 3x3) is applied to each vector in S. Find the transition matrix PBS.

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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Let S = {1, 2, 3} be the standard basis for R³, and let B = {₁, 2, 3} be the basis that results when the linear transformation defined by T(T₁, T2, T3) = (T1₁ + x2, 2x1 − X2 + 4x3, x₂ + 3x3) is applied to each vector in S. Find the transition matrix PB→S.
Transcribed Image Text:Let S = {1, 2, 3} be the standard basis for R³, and let B = {₁, 2, 3} be the basis that results when the linear transformation defined by T(T₁, T2, T3) = (T1₁ + x2, 2x1 − X2 + 4x3, x₂ + 3x3) is applied to each vector in S. Find the transition matrix PB→S.
Let S = {1, 2, 3} be the standard basis for R³, and let B = {₁, 2, 3} be the basis that results when the linear transformation defined by T(T₁, T2, T3) = (T1₁ + x2, 2x1 − X2 + 4x3, x₂ + 3x3) is applied to each vector in S. Find the transition matrix PB→S.
Transcribed Image Text:Let S = {1, 2, 3} be the standard basis for R³, and let B = {₁, 2, 3} be the basis that results when the linear transformation defined by T(T₁, T2, T3) = (T1₁ + x2, 2x1 − X2 + 4x3, x₂ + 3x3) is applied to each vector in S. Find the transition matrix PB→S.
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