





Linear Algebra 6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2...
a) Find a subset of the given vectors that forms a basis for the space spanned by these vectors. b) Express each vector not in the basis as a linear combination of the basis vectors.c) Use the vectors V1, V2, V3, V4, Vs to construct a basis for R4.
3. (12 pts) Find a subset of vectors that forms a basis for the space spanned by v1 = (1, 2, 2, -1), v2 = (-3, -6, -6,3), v3 = (4,9, 9, -4), v4 = (-2,-1,-1,2), v5 = (5,8,9,-5) Then express the other vector(s) as a linear combination of the basis vectors.
3. (12 pts) Find a subset of vectors that forms a basis for the space spanned by Vi = (1, -2,0,3), 02 = (2,-5, -3,6), V3 = (0,1,3,0), 04 = (-2, 1, -4,7), v5 = = (-5, 8,-1, -2). Then express the other vector(s) as a linear combination of the basis vectors.
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Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
15 points) Consider the following vectors in R3 0 0 2 V1 = 1 ; V2 = 3 ; V3 = 1] ; V4 = -1;V5 = 4 1 2 3 = a) Are V1, V2, V3, V4, V5 linearly independent? Explain. b) Let H (V1, V2, V3, V4, V5) be a 3 x 5 matrix, find (i) a basis of N(H) (ii) a basis of R(H) (iii) a basis of C(H) (iv) the rank of H (v) the nullity...
please give the correct answer with explanations, thank you
Let S {V1, V2, V3, V4, Vs} be a set of five vectors in R] Let W-span) When these vectors are placed as columns into a matrix A as A-(V2 V3 r. ws). and Asrow-reduced to echelon form U. we have U - -1 1 013 001 1 state the dimension of W Number 2. State a boss B for W using the standard algorithm, using vectors with a small as...
Let --0) --- () -- () = 0 V = 2 . V = 5 , V3 = 8 . V = 11 (a) Find the reduced row echelon form R = (v1, V, V, val of A = (v1, V2, V3, V4]. (b) Write vs and va as linear combinations of vand va (c) Write V3 and Va as linear combinations of vi and V2. (d) Find a basis for the row space of A. (e) Find a basis...
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.
V1 = 1 , V2= -1 , U3 = , 04 = 1 , 05 = 6 -3 0 | 2 Let S CR5 be defined by S = span(01, 02, 03, 04, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors 01, 02, 03, 04, 05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider the vectors W1 = 14,...