Matrices A and R are defined below. Martrix A is row equivalent to matrix R, that is, A = R. (Do not row reduce A) a) Find a basis for the column space of A. b) Find a basis for the null space of A. c) Suppose T: R5-R4 is the linear transormation given by T(v) - Av. Ideantisy a nonzero vector v that satisfies T(v) = 0. If no such vector exists, write "None". d) Suppose T: R5-R4 is the linear transormation given by T(v) - Av. Does T map R5 onto R4?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 5E
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Matrices A and R are defined below. Martrix A is row equivalent to matrix R, that is, A = R. (Do not row reduce A)

a) Find a basis for the column space of A.

b) Find a basis for the null space of A.

c) Suppose T: R5-R4 is the linear transormation given by T(v) - Av. Ideantisy a nonzero vector v that satisfies T(v) = 0. If no such vector exists, write "None".

d) Suppose T: R5-R4 is the linear transormation given by T(v) - Av. Does T map R5 onto R4?

 

[-7
-4
45
0.
-32
[1
-3
47
--8
42
3
15-
1
--6
1
A =
R =
1
-3
18
1
2
10
-30
40
0.
Transcribed Image Text:[-7 -4 45 0. -32 [1 -3 47 --8 42 3 15- 1 --6 1 A = R = 1 -3 18 1 2 10 -30 40 0.
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