7. Consider the following basis B3 of P2(R) and the standard basis E of P₂ (R) B3 = {1+x², x + x²,1+2x+4x²}, E = {1, x, x²}. (a) Directly from the definition of coordinates, find [4+ 5x²] B3. (b) If [p(x)] B₂ = (c) Find the change of basis matrix PE B3. Use this matrix to solve part (b). (d) Find the change of basis matrix PB3+E. Use this matrix to solve part (a). ? find p(x).
7. Consider the following basis B3 of P2(R) and the standard basis E of P₂ (R) B3 = {1+x², x + x²,1+2x+4x²}, E = {1, x, x²}. (a) Directly from the definition of coordinates, find [4+ 5x²] B3. (b) If [p(x)] B₂ = (c) Find the change of basis matrix PE B3. Use this matrix to solve part (b). (d) Find the change of basis matrix PB3+E. Use this matrix to solve part (a). ? find p(x).
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
![7. Consider the following basis B3 of P2 (R) and the standard basis E of P₂ (R)
B₂ = {1+x², x + x², 1+2x+4x²}, E = {1, x,x²}.
(a) Directly from the definition of coordinates, find [4+ 5x²]B3.
1
-1
2
(c) Find the change of basis matrix PEB. Use this matrix to solve part (b).
(d) Find the change of basis matrix PB+E. Use this matrix to solve part (a).
For the next two questions, given the following two bases for M₂ (R)
9
O
esc
(b) If [p(x)]B3 =
F1
2
F2
59
#
3
80
F3
$
4
A
2
o
F4
find p(x).
%
5
6
F5
6
F6
W
&
7
F7
N
8
DII
F8
759
♫
8
9
F9
7
s
F10
F11
F12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67429e19-8d15-47bc-bbfe-dfa923849540%2F0abfafcb-e570-47d2-b2ec-91b3cf3fb696%2Fmyrggyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7. Consider the following basis B3 of P2 (R) and the standard basis E of P₂ (R)
B₂ = {1+x², x + x², 1+2x+4x²}, E = {1, x,x²}.
(a) Directly from the definition of coordinates, find [4+ 5x²]B3.
1
-1
2
(c) Find the change of basis matrix PEB. Use this matrix to solve part (b).
(d) Find the change of basis matrix PB+E. Use this matrix to solve part (a).
For the next two questions, given the following two bases for M₂ (R)
9
O
esc
(b) If [p(x)]B3 =
F1
2
F2
59
#
3
80
F3
$
4
A
2
o
F4
find p(x).
%
5
6
F5
6
F6
W
&
7
F7
N
8
DII
F8
759
♫
8
9
F9
7
s
F10
F11
F12
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