The linear transform T: V1 → V2 plots the base vectors j and i as follows: T(i) = i +j , TG) = 2i – j A) Find T2 (3i – 4j) and T(3i – 4j) in terms of i and j . B) Find the conversion matrices T2 andT. C) If we use bases (i, j) instead of (i – j, 3i + j), find the conversion matrix T .

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The linear transform T: V → V2 plots the base vectors j and i as follows:
T(i) = i +j , T(j) = 2i – j
A) Find T2 (3i – 4j) and T(3i – 4j) in terms of i and j.
B) Find the conversion matrices T2 andT.
C) If we use bases (i, j) instead of (i – j, 3i + j), find the conversion matrix T
Transcribed Image Text:The linear transform T: V → V2 plots the base vectors j and i as follows: T(i) = i +j , T(j) = 2i – j A) Find T2 (3i – 4j) and T(3i – 4j) in terms of i and j. B) Find the conversion matrices T2 andT. C) If we use bases (i, j) instead of (i – j, 3i + j), find the conversion matrix T
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