1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*. (a) Examine if vector X = (-4,-1,6,12) is in the span{B, C} (b) Examine if vector X = (-4,–1,6,12) is in the span{B, C} 2. (a) Show that the polynomials p, (x)=1+x, P,(x)=1+2xr-x', p,(x)=x+x² are linearly independent. (b) Decide if polynomial q(x)=-1+x is in the span{p, (x), P2 (x), p; (x)} - E, = 0 -1 3. (a) Show that the matrices E, = E, are linearly 1 0 independent. [2 -9 (b) Decide if matrices A=| | 1 2 3 B = [9 -2] are in the span{E,,E,, E;}. 3 4. Examine if functions fi(x)= x, f;(x) =x², f;(x)=x² – 2x are linearly independent.
1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*. (a) Examine if vector X = (-4,-1,6,12) is in the span{B, C} (b) Examine if vector X = (-4,–1,6,12) is in the span{B, C} 2. (a) Show that the polynomials p, (x)=1+x, P,(x)=1+2xr-x', p,(x)=x+x² are linearly independent. (b) Decide if polynomial q(x)=-1+x is in the span{p, (x), P2 (x), p; (x)} - E, = 0 -1 3. (a) Show that the matrices E, = E, are linearly 1 0 independent. [2 -9 (b) Decide if matrices A=| | 1 2 3 B = [9 -2] are in the span{E,,E,, E;}. 3 4. Examine if functions fi(x)= x, f;(x) =x², f;(x)=x² – 2x are linearly independent.
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
![1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*.
(a) Examine if vector X = (-4,-1,6,12) is in the span{B, C}
(b) Examine if vector X = (-4,–1,6,12) is in the span{B, C}
2. (a) Show that the polynomials p, (x)=1+x, P,(x)=1+2xr-x', p,(x)=x+x² are
linearly independent.
(b) Decide if polynomial q(x)=-1+x is in the span{p, (x), P2 (x), p; (x)} -
E, =
0 -1
3. (a) Show that the matrices E, =
E,
are linearly
1 0
independent.
[2 -9
(b) Decide if matrices A=|
| 1
2 3
B =
[9 -2]
are in the span{E,,E,, E;}.
3
4. Examine if functions fi(x)= x, f;(x) =x², f;(x)=x² – 2x are linearly
independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae3c988f-0b7c-45e8-b470-982a890b5fd2%2Fa7eb0b6c-633d-4b1a-a942-01f3b83129d4%2F187zfn_processed.png&w=3840&q=75)
Transcribed Image Text:1. Given vectors B = (1,–2,3,0),C =(-2,1,0,4) in R*.
(a) Examine if vector X = (-4,-1,6,12) is in the span{B, C}
(b) Examine if vector X = (-4,–1,6,12) is in the span{B, C}
2. (a) Show that the polynomials p, (x)=1+x, P,(x)=1+2xr-x', p,(x)=x+x² are
linearly independent.
(b) Decide if polynomial q(x)=-1+x is in the span{p, (x), P2 (x), p; (x)} -
E, =
0 -1
3. (a) Show that the matrices E, =
E,
are linearly
1 0
independent.
[2 -9
(b) Decide if matrices A=|
| 1
2 3
B =
[9 -2]
are in the span{E,,E,, E;}.
3
4. Examine if functions fi(x)= x, f;(x) =x², f;(x)=x² – 2x are linearly
independent.
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