1. Determine whether the following sets form subspaces and justify your answers. (a) {(1, 2): 122...

 

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1. Determine whether the following sets form subspaces and justify your answers. (a) {(1, 2): 122 = 0} in R (b) {(1, 2) |1|-|x2|} in R2 (c) {(x1, x2, x3): x3 = 21 or x3 = 12} in R3 (d) {(x1, x2, x3): 21+ 2+ 3 = 0} in R 2. Determine the null space of each of the following matrices: (a) (b) 2-3 [ 1 -1 -2 -4 6 3 (c) 12 1 3 -4 -1 -1 -1 3 4 1 1 -1 2 (d) 2 2 -3 1 -1 -1 0 -5 1. Determine whether the following sets form subspaces and justify your answers. (a) {(1, 2): 122 = 0} in R (b) {(1, 2) |1|-|x2|} in R2 (c) {(x1, x2, x3): x3 = 21 or x3 = 12} in R3 (d) {(x1, x2, x3): 21+ 2+ 3 = 0} in R 2. Determine the null space of each of the following matrices: (a) (b) 2-3 [ 1 -1 -2 -4 6 3 (c) 12 1 3 -4 -1 -1 -1 3 4 1 1 -1 2 (d) 2 2 -3 1 -1 -1 0 -5

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