8. Given that B = {v1, v2, v3} is a basis for a vector space V .
Determine if S={v1+v2, v2−v3,
v1+2v2+3v3}isalsoabasisforV.
8. Given that B = {V1, V2, V3} is a basis for a vector space V. Determine if S = {V1 + V2, V2 – v3, Vi + 2V2 + 3v3} is also a basis for V.
(4) Let {V1, V2, ..., Vn} be a basis for a vector space V. If w is an element of V whose coefficient vector is the zero vector, show that w must be the zero element.
3. Suppose S = {V1, V2, V3} is a linearly dependent subset of a vector space V. Using only the definition of linear dependence and the span of a set, prove that you can remove one vector from S and still have a set with the same span of the original set.
Is the following statement True or False? If V is a vector space and V1 ≤ V, V2 ≤ V, then V1 ∩ V2 ≤ V. True False
An orthogonal basis for the column space of matrix A is {V1 , V2 ,V3) Use this orthogonal basis to find a QR factorization of matrix A Q = _______ , R = _______
1, U2, v3, U4E IR 1 = 2v2 = 3v3 = v 7. Determine if the set W = 4v4} is a vector space. If it is, find its dimension and a basis
1. Find A if (2A)' = [ : :] 2. Determine if {(x,y) : x - y = 1) is a subspace of vector space V - R 3. Let vi, V2, V3 be three linearly independent vectors in a vector space V. Is the set {v1 - 2v2, 2v2 - 3v3, 3V3 - Vi} linearly independent or linearly dependent? Prove your answer.
In the given circuit, obtain V1, V2, and V3. Assume A = 130 V, B = 110 V, C = 80 V, and D = 140 V. + D - - B + + C- + 12 + + + A V1 13 The unknown voltages V1, V2, and V3 are V V, and V, respectively
- Given: V1 = H. V2 = - - - , V3 = Show that S = {V1, V2, V3} is a basis for Rº and then construct an orthonormal basis {U1, U2, U3}.
Let B = [V1, V2, V3] and B' = [W1, W2, W3] be bases for a vector space V and Vi = W1 + 5W2 – W3 U2 = W1 U3 -W1 - 4w2 – 2w3 If (U)b = (1,-1,2), then the coordinates of v relative to the basis B' are c1 = C2 = and cz