Determine which of the following statements are true.
(a) span{u, v} = span{u + v, u − v},
(b) span{u, v, w} = span{u + v − w, u − 2v + w, 2v − 4u}
(c) span{u, v, 0} = span{u, v}
(d) span{u, v, w} = span{u + v + w, u + 2v + 2w, u − v + w, v + w}
Determine which of the following sets are linearly independent.
(a) {[1 −1 1],[1 0 2],[0 1 1]}
(b) {[1 −1 1],[0 1 1]}
(c) {[1 0 0],[0 1 0],[1 0 1]}
(d) {[1 0 0],[1 0 1]}
(a) t − 1,
(b) 5t − 5,
(c) 5t − 2,
(d) −10t + 2,
(e) 0.
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