= 1(91,y2, y3) 1y1 +y2 + 2y3 2. Let 1, 2, X3 be linearly independent vectors in Rn and let Y1 = 1 t2, y2 2 X3, and y3 3+ x1. Are y1, y2, y3 linearly independent? Prove your answer. 3. Whether the following vectors x 2, x + 1,x-1 are linearly independent in P3. 1 2 3 4. Let A= 2 1-3-2 3 3 0 2 (a) 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 BK n. 6. Let E [x2, x, 1] and F x2 +22 , x 1, 1] be ordered bases of P3. (a) Find the transition matrix representing the change from E to F. (b) Use the transition matrix to find coordinate vector pF with p r - 2x +1. t 1
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#5
![= 1(91,y2, y3) 1y1 +y2 + 2y3
2. Let 1, 2, X3 be linearly independent vectors in Rn and let
Y1 = 1 t2,
y2 2 X3,
and y3 3+ x1.
Are y1, y2, y3 linearly independent? Prove your answer.
3. Whether the following vectors x 2, x + 1,x-1 are linearly independent in P3.
1 2 3
4. Let A=
2 1-3-2
3 3 0 2
(a) 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 BK n.
6. Let E [x2, x, 1] and F
x2 +22 , x 1, 1] be ordered bases of P3.
(a) Find the transition matrix representing the change from E to F.
(b) Use the transition matrix to find coordinate vector pF with p
r - 2x +1.
t
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5c85cb-60d8-4aa4-b6f6-3a8d554b379e%2F7ceeea26-2c10-4b5f-80ce-5bcc4feab884%2F8b505h.jpeg&w=3840&q=75)
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