Let 0 1 1 -1 0 A 0 1 1 1 0 1 2372 0 0 2 0 (a) Find an ordered basis for ran(A), what is dim(ran(A))? (b) A defines a linear transformation T : Rn → Rk by T(x) = Añ. What are n and k? (c) Use the Rank-Nullity theorem to find dim(ker(A)). Then, find a basis for ker(A). (d) Add vectors to the ordered basis for ran(A) you found in (a) to get an ordered basis B for Rk where k is as in (b) (e) Let be the standard basis for Rk. Find Pe→B. (f) For each of the following, find the set of solutions if there are any, if there is no solutions, explain why. Ax= 333 3/2 2 Ay = Az = -1/2 3/2 1002
Let 0 1 1 -1 0 A 0 1 1 1 0 1 2372 0 0 2 0 (a) Find an ordered basis for ran(A), what is dim(ran(A))? (b) A defines a linear transformation T : Rn → Rk by T(x) = Añ. What are n and k? (c) Use the Rank-Nullity theorem to find dim(ker(A)). Then, find a basis for ker(A). (d) Add vectors to the ordered basis for ran(A) you found in (a) to get an ordered basis B for Rk where k is as in (b) (e) Let be the standard basis for Rk. Find Pe→B. (f) For each of the following, find the set of solutions if there are any, if there is no solutions, explain why. Ax= 333 3/2 2 Ay = Az = -1/2 3/2 1002
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with solution with steps for parts d,e,f

Transcribed Image Text:Let
1
0
1
2
Ο
1
−1 0
3 0
A
0
1 1 -1 2
-
1
012
0
(a) Find an ordered basis for ran(A), what is dim(ran(A))?
(b) A defines a linear transformation T : Rn → Rk by T(Ã)
= Ax. What are n and k?
(c) Use the Rank-Nullity theorem to find dim(ker(A)). Then, find a basis for ker(A).
(d) Add vectors to the ordered basis for ran(A) you found in (a) to get an ordered basis B
for Rk where k is as in (b)
(e) Let be the standard basis for Rk. Find Pe→ß.
(f) For each of the following, find the set of solutions if there are any, if there is no solutions,
explain why.
[4
3
3/2
2
0
Ax
=
Ay =
Az=
3
-1/2
0
3
3/2
2
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