1. Determine if the following vectors are linearly dependent or independent. Find an exact (non- trivial) linear combination of the vectors that gives the 0-vector (0,0,0) if they are dependent. V₁ = (1, 0, -1) V₂ = (-1, 1, 2) V3 = (-3, 1, 4)

The set of vectors {(1,1,0,0),(0,-1,0,0),(0,0,1,1),(1,0,1,1)} is linearly dependent. What is a valid expression of the last vector as a linear combination of the others? a. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)-(0,0,1,1) b. (1,0,1,1)=(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) c. (1,0,1,1)=-(1,1,0,0)+(0,-1,0,0)+(0,0,1,1) d. (1,0,1,1)=2(1,1,0,0)+2(0,-1,0,0)+2(0,0,1,1)

Let u = (2,0), v = (5,4), and w = (2,3). Find the vector that satisfies 10u-v+x = 8x+w.

4. ) Determine whether the following three vectors are linearly independent or inearly dependent. v₁ = (3,3, 0, 2), v₂ = (0, 2, 3, 1), V3 (3, 0, -2, -1). Hint: You can turn them into column vectors. =

Let u+v = (3, –2) and u – v = (-4, –3). (a) Find u and v. (b) Draw the vectors u, v, - u, - v, u+v, (u – v), (-u+v), (-u – v) in the single ry-plane.

Let be the vector with initial point (8, 1) and terminal point (6,5). Express as a linear combination of the standard unit vectors. Ov=4i-2j 05-21-47 Ov=2i+4j Ov=-21-4j Ov=-2+47 O None of the above.