Consider the following matrix: 1 4 -2 A = -1 4 -6 3 2 Determine which of the following sets of vectors are bases of the column space of A. 1) 2) 3) 4) 372 A 321 = -18 ·EW 5) -10 661 6) -6 7) 8) -1 9) -4 8) 9) .....p and Hint. If V1,..., V, and w₁,..., W, are vectors in a vector space V, then Span (V1, ..., V,) = Span (W₁,..., w) if and only if v, E Span (w₁,..., w,) for each i = 1,. w, Span (V1,..., Vp) for each j = 1,..., 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 < Previous Next > Reset
Consider the following matrix: 1 4 -2 A = -1 4 -6 3 2 Determine which of the following sets of vectors are bases of the column space of A. 1) 2) 3) 4) 372 A 321 = -18 ·EW 5) -10 661 6) -6 7) 8) -1 9) -4 8) 9) .....p and Hint. If V1,..., V, and w₁,..., W, are vectors in a vector space V, then Span (V1, ..., V,) = Span (W₁,..., w) if and only if v, E Span (w₁,..., w,) for each i = 1,. w, Span (V1,..., Vp) for each j = 1,..., 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 < Previous Next > Reset
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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Transcribed Image Text:Consider the following matrix:
1
4
-2
A =
-1
4 -6
3
2
Determine which of the following sets of vectors are bases of the column space of A.
1)
2)
3)
4)
372
A
321
=
-18
·EW
5)
-10
661
6)
-6
7)
8)
-1
9)
-4
Transcribed Image Text:8)
9)
.....p and
Hint. If V1,..., V, and w₁,..., W, are vectors in a vector space V, then Span (V1, ..., V,) = Span (W₁,..., w) if and only if v, E Span (w₁,..., w,) for each i = 1,.
w, Span (V1,..., Vp) for each j = 1,...,
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
< Previous
Next >
Reset
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