Different sets of vectors

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1. (a) Give three different sets of vectors that span R2. (b) Give three different bases R2. (c) Give three different sets of vectors that span R®. (d) Give three different bases R®. 2. Determine if the following statements are true or false. Justify your work. [14 -3] [4 (a) | 0 | € Span 31,13 |—2 4] |3 [4 -3 -3 (b) |4| € Spang |-1|,|-5 2 —4 4 3. Determine if the following sets are linearly independent or not. If not, reduce the set to a linearly independent set. Justify your work. 0 0] [-1] [-1 —o| |-3| |3 8 @ Tol] 2 2] |-1| |1 0 5] [3 2 ®) { [2], |-8],]|6 7] [a] |15 4. Determine if the following statements are true or false. Justify your work. (a) If {#h, ++, Us} is a linearly independent subset of R™, then the following set of vectors is linearly independent. {= + 30, — Ts, —30 — 20, —37, — 30, — 5} (b) If {¢h,— , 7s} is a linearly independent subset of R”, then the following set of vectors is linearly independent. {20 + Ty + Ts, 20, — By — 203, —20 + 305 + 573}