Let V, W be finite dimensional vector spaces and T: V → W be a linear transformation. Let A = [T]½ and B= [T], where B, B' and Y, Y' are bases of V and W respectively. Let R be the RREF of A and R' be the RREF of B. (a) Prove that the number of leading ones in R is equal to the number of leading ones in R'. (b) Show by example, that R and R' need not be equal.
Let V, W be finite dimensional vector spaces and T: V → W be a linear transformation. Let A = [T]½ and B= [T], where B, B' and Y, Y' are bases of V and W respectively. Let R be the RREF of A and R' be the RREF of B. (a) Prove that the number of leading ones in R is equal to the number of leading ones in R'. (b) Show by example, that R and R' need not be equal.
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 V, W be finite dimensional vector spaces and T : V → W be a linear transformation. Let A
[T], and B = [T. where B, B' and
Y, Y' are bases of V and W respectively.
Let R be the RREF of A and R' be the RREF of B.
(a) Prove that the number of leading ones in R is equal to the number of leading ones in R'.
(b) Show by example, that R and R' need not be equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0290c84-3759-4118-bbff-0e3c336ac19c%2F668b8798-65a8-4d31-bc4c-1a75143e3287%2Fdwe1cej_processed.png&w=3840&q=75)
Transcribed Image Text:Let V, W be finite dimensional vector spaces and T : V → W be a linear transformation. Let A
[T], and B = [T. where B, B' and
Y, Y' are bases of V and W respectively.
Let R be the RREF of A and R' be the RREF of B.
(a) Prove that the number of leading ones in R is equal to the number of leading ones in R'.
(b) Show by example, that R and R' need not be equal.
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