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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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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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: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
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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