a4 a1 Let V1 (3).. b4 be four vectors in R³. b₁ b₂ V3 = C1 C2 C4 a1 a2 a3 a4 If we reduce the matrix A = b₁ b₂ b3 b4 to reduced echelon form, we get the following matrix: C1 C2 C3 C4 /1 0 0 3 0 1 0 5 0 0 17, Which one of the following statements must be true? Select one alternative: The set {V₁, V2, V3} is linearly dependent. v4 is a linear combination of V₁, V2₂, and V3 The set {V₁, V2, V3, V4} is linearly independent. V3 is a linear combination of v₁ and v2. = V2 = a2 az b3 C3 V4 =

Let A= {a;.a2,a3} and B = {b,.b2.b3} be bases for a vector space V, and suppose a, = 5b, - – 2b3. a. Find the change-of-coordinates matrix from A to B. b. Find (xlg for x= 5a, + 6a2 + az. a P B-A b. xlg =0 (Simplify your answer.)

Multiply the matrices A and B. [3 2 A = 2 5 3 4 5 1 4 3 2 1 Show your work in the space provided below. B =