Consider the following matrix: 1 4 -2 A = -1 4 -6 3 2 4 Determine which of the following sets of vectors are bases of the column space of A. 1) 2) 3) 4) = 372 32 - 330 -7 -18 5) -10 -10 » {}{} 6) 7) 8) 9) 7) 8) 9) .....p and Hint. If V1,..., V, and w₁,..., W, are vectors in a vector space V, then Span (V1, ..., Vp) = Span (W₁,..., w) if and only if v, E Span (w₁,..., w,) for each i = 1,. w, Є Span (V1, ..., Vp) for each j = 1,..., r How to enter the solution. Enter numbers corresponding to sets which are bases separating them by commas. For example, if you obtain that the sets 1, 3, 5, and 6 are bases then you should enter the answer as follows: Do not forget about commas between the numbers. 1, 3, 5, 6 Enter numbers corresponding to all sets which are bases of the columm space of A: Submit Reset
Consider the following matrix: 1 4 -2 A = -1 4 -6 3 2 4 Determine which of the following sets of vectors are bases of the column space of A. 1) 2) 3) 4) = 372 32 - 330 -7 -18 5) -10 -10 » {}{} 6) 7) 8) 9) 7) 8) 9) .....p and Hint. If V1,..., V, and w₁,..., W, are vectors in a vector space V, then Span (V1, ..., Vp) = Span (W₁,..., w) if and only if v, E Span (w₁,..., w,) for each i = 1,. w, Є Span (V1, ..., Vp) for each j = 1,..., r How to enter the solution. Enter numbers corresponding to sets which are bases separating them by commas. For example, if you obtain that the sets 1, 3, 5, and 6 are bases then you should enter the answer as follows: Do not forget about commas between the numbers. 1, 3, 5, 6 Enter numbers corresponding to all sets which are bases of the columm space of A: Submit Reset
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...
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Transcribed Image Text:Consider the following matrix:
1
4
-2
A = -1
4
-6
3
2
4
Determine which of the following sets of vectors are bases of the column space of A.
1)
2)
3)
4)
=
372 32 - 330
-7
-18
5)
-10
-10
» {}{}
6)
7)
8)
9)
Transcribed Image Text:7)
8)
9)
.....p and
Hint. If V1,..., V, and w₁,..., W, are vectors in a vector space V, then Span (V1, ..., Vp) = Span (W₁,..., w) if and only if v, E Span (w₁,..., w,) for each i = 1,.
w, Є Span (V1, ..., Vp) for each j = 1,..., r
How to enter the solution.
Enter numbers corresponding to sets which are bases separating them by commas. For example, if you obtain that the sets 1, 3, 5, and 6 are bases then you should enter the
answer as follows:
Do not forget about commas between the numbers.
1, 3, 5, 6
Enter numbers corresponding to all sets which are bases of the columm space of A:
Submit
Reset
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