3. Consider these vectors in R²: V₁ = -[4] (a) Find coefficients to express the vector 3 V2 - H 3 as a linear combination of v₁ and v2. (b) Given an arbitrary vector T [3] show that it can be written as a linear combination of v₁ and v2. (Find formulas for the coefficients a and az in terms of x and 20 y.) (c) Describe span {V1, V2} within R2 using words and pictures. (d) Are the vectors (V1, V2} linearly independent? Justify your answer. (e) Is the matrix V1 V2 invertible? If so, find its inverse. How is this connected to your work above? Vi

Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.

Solve for the vector x in terms of the vectors a and b. (If needed, use BOLD vector form on calcPad Vector menu.) - b = 8(x + a) 3(3a - b) X = x + 3a

10. (a) The non-zero vectors a, b andc are such that axb exa. Given that b -e, find a linear relationship between a, b and c. (b) The variable vector v satisfies the equation vx(i-3k)= 2j. Find the set of vectors v and [(b) v = HER] fully describe this set geometrically.