3. [10 points] (a) Determine if the vectors vi (1,2,-1, (3,8,0), v ,1,1) span R3. |...
Question 5: Multiple Choices Assume that vi,2,ig are vectors in R3. Let S span ,02,s and let A be the matrix whose columns are these vectors. Assume that 1 -1 1 0 0 0-3a +b-2c We can thus conclude that A. {6,6,6) is L1. B. The point (1,1 - 1) is in the span of (o,2,s) C. The nullity of A is 2 D. The rank of A is 3 E. B and C are both correct
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
1. Determine whether the given vectors span R3 v - (5,5,5), v2 (0, 0,-1), v3 (0,-1,-1)
5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1 = (1,1,1), V2 = (1,0,1), V3 = (3,2,1) coincides with R. (b) Determine if b= is in the column space of A = 13 1 11 2 0 1 . If yes, write bas a linear 1 1 1] combination of columns of A.
Let the vectors a = <1,2,3>, b= <1,1, 1 > and c = <1,2, 1 > a) Determine whether the three are coplanar None of these 4 0.71 0.74 no b) Find the volume of the parallelepiped form c) Find the unit vector orthogonal to both ved d) Find the angle between the vectors a and 22.26 bunded to 2 decimal points) 12:21 e) Find the component of the vector a along 39.51 -1 ge
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
45 points) Consider the following vectors in R3 2 0 0 2 2 Vi = 1 ;02 31; V3 = 11:04 = -1 ; Us = 4 2 2 3 (c) Find a basis of R3 among V1, V2, V3, V4, V5, and call it basis V. (d) Is vs Espan{V1, V2, 03, 04}? Explain. (e) Find the coordinates of us with respect to the basis V.
Consider the following vectors: 2 2 2 10 -3 For each of the following vectors, determine whether it is in span (a, b, cj. If so, express it as a linear combination using a, b, and c as the names of the vectors above 14 < Select an answer > v2 = 216
Consider the following vectors: 2 2 2 10 -3 For each of the following vectors, determine whether it is in span (a, b, cj. If so, express...
5. (20 pts. each) Let V -span((1a, -1,0,-4).(-1,1,1,3)). a. Express Vi as a span of basis vectors. b. Let b - (3, 0, 1, -2). Present b as b - p+ z, such that p e V and z e vi
answer in following concerning span and linear combinations a) describe circumstance in which the span vectors {u,v,w} is a plane in R3 b) determine if given vector w is a linear combination of vector v1 = <1,2> and vector v2 = <1,3>. If it is, find a, b such that vector w = aV1 + bV2 (v1,v2 are vectors). Use vector w = <1,-5>