(a) (5 points.) Let W CW CW CW3 be distinct subspaces of R? True/False (Justify your...
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
1) Determine if w is in the subspace spanned by v1, v2, v3 2) Are the vectors v1, v2, v3 linearly dependent or independent? justify your answer Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
(1 point) Are the following statements true or false? ? 1. If W = Span{V1, V2, V3 }, and if {V1, V2, V3 } is an orthogonal set in W, then {V1, V2, V3 } is an orthonormal basis for W. ? 2. If x is not in a subspace W, projw(x) is not zero. then x ? 3. In a QR factorization, say A = QR (when A has linearly independent columns), the columns of Q form an orthonormal...
Question 2. (15 pts) Let Vi= (-3 0 6)", v2= (-2 2 3)", V3= [0 - 6 3)", and w= [1 14 9)? (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors Vi, V2, V3 linearly dependent or independent? Justify your answer.
Problem 5: Let V and W be vector spaces and let B = {V1, V2, ..., Un} CV be a basis for V. Let L :V + W be a linear transformation, and let Ker L = {2 € V: L(x)=0}. (a) If Ker L = {0}, show that C = {L(v1), L(02), ..., L(vn) } CW is a linearly independent set in W. (b) If C = {L(01), L(V2),..., L(Un)} C W is a linearly independent set in W,...
Question 2. (15 pts) Let vi= (-3 0 6)", V2= (-2 2 317, V3= [0 - 6 3)", and w=(1 14 9) (1). Determine if w is in the subspace spanned by va, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer.
Q10 10 Points Please answer the below questions. Q10.1 4 Points Let m, n EN\{1}, V be a vector space over R of dimension n and (v1,..., Vm) be an m tuple of V. (Select ALL that are TRUE) If m > n then (v1, ..., Vy) spans V. If (01,..., Vm) is linearly independent then m <n. (V1,..., Um) is linearly dependent if and only if for all i = 1,..., m we have that Vi Espan(v1,..., Vi-1, Vi+1,...,...
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...
Let v1= [−3 0 6]T , v2= [−2 2 3]T , v3= [0 − 6 3]T , and w= [1 14 9]T . (1). Determine if w is in the subspace spanned by v1, v2, v3. (2). Are the vectors v1, v2, v3 linearly dependent or independent? Justify your answer.
Please answer me fully with the details. Thanks! True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linearly independent subset of (1) Let V bea vector spacе, аnd let dim(V) V. then n < т. (2) Let V and W be vector spaces, and suppose that T : V -+ W is a linear transformation. If there are vectors i, 2, ..., Tj in V such that the vectors T(),T(T2),...,T(vj) span W, then the...