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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Question

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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