MAT 242 Written Homework #3 EP4.2, 4.3 / H4.2, 4.3 Due: March 15 Solve the following problems, showing any necessary work. 2 1 1 3 1. [1 point] Let W be the subspace spanned by , . Which of the following vectors are in 2 1 2 1 W ? (Note that the number of correct answers might be zero, one, two, three, or four.) 7 15 20 20 1 15 5 15 , , , 24 12 17 16 6 8 12 16 1 2 4 3 2 2 2 1 2. Let ~v1 = , ~v2 = , ~v3 = , and ~v4 = . 3 1 3 3 2 1 1 1 a. [1 point] The set {~v1 , ~v2 , ~v3 , ~v4 } is linearly dependent. Find a nontrivial linear combination of these vectors that adds up to ~0. 0 1 b. [1 point] Is the vector in the span of S? Justify your answer. 3 4 2 1 6 1 2 1 1 3 1 2 3. [1 point] Let S = , , , , . Find a basis for the subspace W spanned 2 3 2 6 1 3 3 9 2 3 by S, and the dimension of W