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...

linear algebra about matrix


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}