19. r₁ = 2 - 3x + x², 1₂ 20. s₁ = 1 + x², S₂ = x + x³, S3 = x + x², 54 = 1 + x³, for P₁ le 1 and find a basis for M32. What is dim M
19. r₁ = 2 - 3x + x², 1₂ 20. s₁ = 1 + x², S₂ = x + x³, S3 = x + x², 54 = 1 + x³, for P₁ le 1 and find a basis for M32. What is dim M
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 34EQ
Related questions
Question
Do the given
(Number 20 on picture)
![/VECTOR SPACES
27.
26.
19. - -
22.
20. s₁ = 1 + x², S₂ = x + x²³₂ $3 = x + x², S4 = 1 + x³, for P
S3
21.
Follow the pattern of Example 4 and find a basis for M32. What is dim M32
23.
¹₁ = 2 − 3x + x², r₂ = 4 + 3x − 2x², r3
24.
25.
Same question as Exercise 21 for M22-
Same question as Exercise 21 for M,
*
mn
Determine if the matrices
M₁ = [18].
form a basis for M22-
Same question as Exercise 24 for
- [
N₂
N3
N₁-[2-1]. N₁ - [2
Let W be the subspace of C[0, 1] spanned by S = (sin² x, cos² x, cos 2x
(a) Explain why S is not a basis for W.
(b) Find a basis for W.
(c) What is dim W?
№₁
27
1
2
-2 -2
-1
0
M₂ =
2
[!]
[
= 9x - 4x², for P2
-23
20
In Exercises 27-32, find a basis for, and the dimension of, the null sp
the given matrix.
M3
11
MA
- M-O
28.
2
AN
1 -1
A](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92dd192b-2b85-4e23-91c3-a8e23aec13bb%2F8f4eed22-7c97-41d7-816a-22ddf83491ff%2Fj9lec8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:/VECTOR SPACES
27.
26.
19. - -
22.
20. s₁ = 1 + x², S₂ = x + x²³₂ $3 = x + x², S4 = 1 + x³, for P
S3
21.
Follow the pattern of Example 4 and find a basis for M32. What is dim M32
23.
¹₁ = 2 − 3x + x², r₂ = 4 + 3x − 2x², r3
24.
25.
Same question as Exercise 21 for M22-
Same question as Exercise 21 for M,
*
mn
Determine if the matrices
M₁ = [18].
form a basis for M22-
Same question as Exercise 24 for
- [
N₂
N3
N₁-[2-1]. N₁ - [2
Let W be the subspace of C[0, 1] spanned by S = (sin² x, cos² x, cos 2x
(a) Explain why S is not a basis for W.
(b) Find a basis for W.
(c) What is dim W?
№₁
27
1
2
-2 -2
-1
0
M₂ =
2
[!]
[
= 9x - 4x², for P2
-23
20
In Exercises 27-32, find a basis for, and the dimension of, the null sp
the given matrix.
M3
11
MA
- M-O
28.
2
AN
1 -1
A
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