(p) X {(x1, 22, 3)| x1- 2-23} is orthogonal to Y = {(y1,y2, y3) 1y1+y2+2y3 T 2. Let 1, 2, 3 be linearly independent vectors in R" and let y1 x1 ax2, Y2 = x2 + X3, and y3=3+x1 Are y1, y2, 3y3 linearly independent? Prove your answer. 3. Whether the following vectors x + 2,x +1, 1 are linearly independent in P3. 1 2 3 4 2 1-3 2 3 3 0 4. Let A = 2 Find a basis of N(A),/row space of A/ column space of A. (b) Find nullity (A) and rank A. 5. Let A and B be two n xn matrices. Suppose that AB On. Show that rank A + rank B
(p) X {(x1, 22, 3)| x1- 2-23} is orthogonal to Y = {(y1,y2, y3) 1y1+y2+2y3 T 2. Let 1, 2, 3 be linearly independent vectors in R" and let y1 x1 ax2, Y2 = x2 + X3, and y3=3+x1 Are y1, y2, 3y3 linearly independent? Prove your answer. 3. Whether the following vectors x + 2,x +1, 1 are linearly independent in P3. 1 2 3 4 2 1-3 2 3 3 0 4. Let A = 2 Find a basis of N(A),/row space of A/ column space of A. (b) Find nullity (A) and rank A. 5. Let A and B be two n xn matrices. Suppose that AB On. Show that rank A + rank B
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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4a
![(p) X
{(x1, 22, 3)| x1- 2-23} is orthogonal to Y = {(y1,y2, y3) 1y1+y2+2y3
T
2. Let 1, 2, 3 be linearly independent vectors in R" and let
y1 x1 ax2,
Y2 = x2 + X3,
and y3=3+x1
Are y1, y2, 3y3 linearly independent? Prove your answer.
3. Whether the following vectors x + 2,x +1,
1 are linearly independent in P3.
1 2 3
4
2 1-3 2
3 3 0
4. Let A =
2
Find a basis of N(A),/row space of A/ column space of A.
(b) Find nullity (A) and rank A.
5. Let A and B be two n xn matrices. Suppose that AB On. Show that
rank A + rank B <n.
6. Let E = [x2, x, 1] and F = x2 +2x, 1, 1] be ordered bases of P3.
(a) Find the transition matrix representing the change from E to F
x2 -2
(b) Use the transition matrix to find coordinate vector [plF with p
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5c85cb-60d8-4aa4-b6f6-3a8d554b379e%2Fb723b628-b383-4955-bd59-5ad3ece8f7a0%2Fu717rzq.jpeg&w=3840&q=75)
Transcribed Image Text:(p) X
{(x1, 22, 3)| x1- 2-23} is orthogonal to Y = {(y1,y2, y3) 1y1+y2+2y3
T
2. Let 1, 2, 3 be linearly independent vectors in R" and let
y1 x1 ax2,
Y2 = x2 + X3,
and y3=3+x1
Are y1, y2, 3y3 linearly independent? Prove your answer.
3. Whether the following vectors x + 2,x +1,
1 are linearly independent in P3.
1 2 3
4
2 1-3 2
3 3 0
4. Let A =
2
Find a basis of N(A),/row space of A/ column space of A.
(b) Find nullity (A) and rank A.
5. Let A and B be two n xn matrices. Suppose that AB On. Show that
rank A + rank B <n.
6. Let E = [x2, x, 1] and F = x2 +2x, 1, 1] be ordered bases of P3.
(a) Find the transition matrix representing the change from E to F
x2 -2
(b) Use the transition matrix to find coordinate vector [plF with p
1
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