Problem 4. Consider the vectors v₁ = 2 1 -----· V2 = (b) Determine which of the vectors a = (a) Find a basis for Col A, where A = [V1 V2 V3 V₁]. 4 [] -3 -2 5 coordinate vector in the basis of Span{V1, V2, V3, V4} from part (a). (c) Do the vectors V2, V3, and v4 span R³? Explain. V3 = and b = -5 2 1 3 H] 0 = and V4 is in Span{V1, V2, V3, V₁} and find its

5.) Sketch the given vectors Vand W. On your sketch, draw in v v+w, and v-w. OV=(2, 1) and W=(1, 2) by v= (0₁4) and w = (2₁-1) v=(2,3₁-6) ond w=(-1,1,1)

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

Explain the Combination of basis vectors.