Let P2(x) be the vector space of polynomials with real coefficients of degree at most 2 with the or- dered bases B2 = {x+ x + 1, x2 + x,x – 1} and B1 = {2x? + 3x + 1,2x² + 2x + 1, –3x – 6x – 2} . Then which of the following is the transition matrix [M from the basis B1 to the basis B2? -3 2 -1 (a) 3 -1 1 7 -4 2 2 1 -5 (b) 0 1 2 10 -3 -3 3 7 (c) -1 -4 -1 1. 2 -2 1 5 (d) 0 1 2 1 0 3 - -3 3 7 (e) 3 2 0 2.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 13EQ
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Let P2(x) be the vector space of polynomials with real coefficients of degree at most 2 with the or-
dered bases B2 = {x? +x+ 1, x² + x,x – 1} and B1 = {2x2 +3x+ 1,2.1² +2x + 1, –3x? – 6x – 2}.
Then which of the following is the transition matrix [M from the basis Bị to the basis B2?
-3 2
-1
(a)
3
-1 1
7 -4 2
2 1 -5
(b)
0 1 2
10 -3
-3 3
7
(c)
-1 -4
-1
1.
-2 15
(d)
0 1 2
1
0 3
-3 3
7
(e)
3
2 0
2 -1
2.
2.
2.
Transcribed Image Text:Let P2(x) be the vector space of polynomials with real coefficients of degree at most 2 with the or- dered bases B2 = {x? +x+ 1, x² + x,x – 1} and B1 = {2x2 +3x+ 1,2.1² +2x + 1, –3x? – 6x – 2}. Then which of the following is the transition matrix [M from the basis Bị to the basis B2? -3 2 -1 (a) 3 -1 1 7 -4 2 2 1 -5 (b) 0 1 2 10 -3 -3 3 7 (c) -1 -4 -1 1. -2 15 (d) 0 1 2 1 0 3 -3 3 7 (e) 3 2 0 2 -1 2. 2. 2.
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