11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a + b – c + d = 0. (а) {(1,0, 0, —1), (0, 1,0, — 1), (0, 0, 1, 1)} (b) {(1,0,0, –1), (0, 1, 0, –1)} (c) {(1,0,0, –1), (0, 1,0, –1), (0,0, 1, –1), (0, 1, – 1,0)} (d) {(1,0,0, –1), (0, 1,0, –1), (0, 1, –1,0)} (е) {(1,0, —1,0), (0, 1,0, — 1), (0, 0, 1, —1)} 6. 6. 6.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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11. Find a basis of the following subspace of R*.
all vectors of the form (a, b, c, d) where a + 6 – c + d = 0.
(a) {(1,0,0, –1), (0, 1,0, –1), (0,0, 1, 1)}
(b) {(1,0,0, –1), (0, 1,0, –1)}
(с) {(1,0, 0, —1), (0, 1,0, — 1), (0, 0, 1, —1), (0, 1, —-1,0)}
(d) {(1,0,0, – 1), (0, 1, 0, –1), (0, 1, – 1,0)}
(e) {(1,0, –1,0), (0, 1,0, –1), (0,0, 1, –1)}
W
%3D
6.
6.
Transcribed Image Text:11. Find a basis of the following subspace of R*. all vectors of the form (a, b, c, d) where a + 6 – c + d = 0. (a) {(1,0,0, –1), (0, 1,0, –1), (0,0, 1, 1)} (b) {(1,0,0, –1), (0, 1,0, –1)} (с) {(1,0, 0, —1), (0, 1,0, — 1), (0, 0, 1, —1), (0, 1, —-1,0)} (d) {(1,0,0, – 1), (0, 1, 0, –1), (0, 1, – 1,0)} (e) {(1,0, –1,0), (0, 1,0, –1), (0,0, 1, –1)} W %3D 6. 6.
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