-2 2 2. Let A = Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the equation PT AP = D, where D is a diagonal matrix, holds. 3. Suppose V and W are vector spaces over a field F. If L : V → W is a linear transformation, then show that ker(L) is a subspace of V. Give an example of a transformation to illustrate this result by considering V = P2 and W = P3, where P2 and P3 are sets of polynomials with degrees less than or equal to 1 and 2, respectively.
-2 2 2. Let A = Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the equation PT AP = D, where D is a diagonal matrix, holds. 3. Suppose V and W are vector spaces over a field F. If L : V → W is a linear transformation, then show that ker(L) is a subspace of V. Give an example of a transformation to illustrate this result by considering V = P2 and W = P3, where P2 and P3 are sets of polynomials with degrees less than or equal to 1 and 2, respectively.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
answer item 3 only
Transcribed Image Text:-2 2
2. Let A =
Find a matrix P that orthogonally diagonalizes A. Then, verify that
1
the equation PT AP = D, where D is a diagonal matrix, holds.
3. Suppose V and W are vector spaces over a field F. If L : V → W is a linear transformation,
then show that ker(L) is a subspace of V. Give an example of a transformation to illustrate
this result by considering V = P2 and W = P3, where P2 and P3 are sets of polynomials
with degrees less than or equal to 1 and 2, respectively.
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