(1) Determine whether each set of vectors is linearly independent or linearly dependent by the method given: 0 Inspection: By observing and thinking about the vectors, you can determine if they are independent or not. Provide a one or two sentence justication and any pictures you deem helpful for understanding {if you wish; pictures are not required}. 0 Algebra: Explicitly nd all the linear combinations of vectors which yields the zero vector and tell whether the vectors are or are not independent. How to do this {while you know how to do this, we never did this explicitly in class): 1. Form an augmented matrix with columns equal to the vectors and augment column of zero 2. Row reduce to RREF If nonzero solution (incl. many solutions or no solution} exists > linear dependence If only zero solutions {unique solution with all zeros in augment column) exist > linear independence (a) Algebra: 1 3 5 do = 2 (1.1 = 2 *2 = 2 3 I 1 I Homework Assignment #5 2 (b) Inspection: 1 4 10C| do = 2 J] = 8 d2 = 2m 3 12 30C| (c) Algebra: 3 1 '1 do = 1 51 = 3 *2 = 1 1 0 0 (d) Inspection: l _ 2 a _ 7 gm _ 1 a1 _1 (1'2 = any other vector (e) Algebra; 1 8 '4 - _ 2 - _ 4 ~ 2 D 3 a1 _ 2 2 2 4 1 4 (2) Compute each vector below. Be sure to show your computation or justification. (a) Compute the point in the span of ONE closest to (b) Compute the point in the span of { 1001 }closest to 110 (c) Compute the point in the span of { ? , 2] } closest to 1 (d) Compute the point in the span of { 2 } closest to ON HOK N 2 (e) Compute the point in the span of { 4 } closest to