Let U=span{ū, ,ū,,ūz and Û=span{u ,u,,u where ū,=(1,0,0,0), ū,=(0,1,1,0), ū,=(0,1,1,1) and u,=(1,0,0,1), u,=(1,1,0,0), u,=(0,0,1,1). Determine the basis and dimension of U & Û.

Q: Let U=span u, ,ū2, ūz and Ü=span{ú, ,ú2,úz where ü,=(1,0,0,0), ủ,=(0,1,1,0), ủ,=(0,1,1,1) and…

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Q: Let U=span{uq ,U2,U3} Û=span {u, ,u,,u,} where ū,=(1,0,0,0), ū,=(0,1,1,0), ū,=(0,1,1,1) and…

A: (a) Given vectors are u1^→=1,0,0,1,u2^→=1,1,0,0,u3^→=0,0,1,1.   Consider U^=spanu1^→, u2^→, u3^→.…

Q: Let u =(5,5,0) and v=(,5,5,(5sqrt2). Compute |u*v|

A: Approach to solving the question: Detailed explanation: Examples: Key…

Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: Let w= (-1,4,15), v = (1, 2, 8), v = (3, 0,1). Does w belong to span(v,,v,)? If yes, then write the…

A: We will find out the required solution.

Q: Let U​ =​{1, 2, 3, 4, a, b, c, d, e​}, E​ =​{1, 3, 4, c, d, e​},F​ =​{1, 2, b, c​}, and G​ =​{1, 2,…

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Q: Write v as a linear combination of u, u2, and u3, possible. (If not possible, enter IMPOSSIBLE.) =…

A: We will find out the required value.

Q: Suppose that u, v, and w are vectors such that cu, V) = 3, cv, w> = – 4, cu, wɔ = 7, ||u||= 1 ||v||=…

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Q: Let W1=span{(1,1,0),(-1,1,0)} and W2=span{(1,0,2),(-1,0,4)} Proove W1+W2=R^3

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Q: If u=(2,4)�=(2,4)  and v=(3,−4)�=(3,−4)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: If u=(1,4)�=(1,4)  and v=(3,2)�=(3,2)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: 2. Assume u = Z, and let A B = {..., -6, -4, -2,0,2, 4, 6,...} {-9, -6, -3,0, 3, 6, 9,...} {...,…

A: According to guidelines we can solve only first three subparts and rest part can be reposted…

Q: Consider the vectors u1 = (1, 2, 1), u2 = (0, 3, 2) and u3 = (−2, 1, 1). Determine whether the set S…

A: The objective of this question is to determine whether the set of vectors S = {u1, u2, u3} spans the…

Q: Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for…

A: a)b)c)d)

Q: Let U=span(ū, ,ū,,ū and Û=span {u, ,u,, where ü,=(1,0,0,0), ū,=(0,1,1,0), ủ,=(0,1,1,1) and…

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Q: determine whether (1, -3, -3) belongs to the span of {(1, -1, 1), (1, 1, -1), (-2, 2, -2)}

A: write all 3 vectors in the matrix A=11-2-1121-1-2 the vector b is b=1-3-3 if the system Ax=b is…

Q: Let P3 is the vector space of polynomials of the degrees3,Consider the polynomials…

A: Given :  P3 is the vector space of polynomials of degree less than or equal to 3. To prove :  We…

Q: Let u= (1, 1, 4, 5), v = (1,4, -4,9) and w = (3, 1, 2, 3). Evaluate: a) dx2 dx3dx4(u, v, w) = b)…

A: Step 1: Step 2:

Q: Define' a vector to contain 2 components: (a,b) where a a rational number, b is an irrational…

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Q: Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are…

A: a) Given that v1=-2,2,1,v2=-8,7,4,v3=-29,25,14,w=6,6,1. It is required to find whether w is in…