Suppose v1, V2,..., Vm E V. Prove that {v1, v2, ..., Um} = (span(v1, v2, ..., Um))-.

Q: Let 2 = (-8,1) and To (-7, -2) Compute the following vector B Prijz To projections.

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Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: Find projs u. S = span { projs u = 0 1 3 4 1 4 H[:)--[:] 1 = 0 6 1 8

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Q: A - [4 = 2 5 5 c=[-³3 C - 1 3 2 3] 0 - 2 1 B = D= 1 5 6 1 0 - 8 2 - 4 5 0 - - 3 1 2

A: Given A=4-1023-2-521, B=15-162-3104, C=51-30 and D=135-10-2 To find-  (a) 5A-3B (b) BD

Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

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Q: Find the projection of u = onto v = .

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Q: 2 -·---·--· , = 3 II. Let v₁ = Is w in span{v1, V2, V3}? = 2 and w= 1 2

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Q: Find the length of the vector x=x= |x|=|x|=

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Q: Find the projection of u = onto v = . projuv =

A: We can find the projection in two form one is in scalar form and other is vector form. here i give…

Q: Suppose v1, v2, v3, v4 span a vector space ?. Prove that the list v1 − v2, v2 − v3, v3 − v4, v4 also…

A: Let V be the vector space Since v1,v2,v3,v4 span the vector space V.

Q: (b) Let v₁ = (-2, 1,5), v₂ = (0, 1,4), V3 = (-2,4, 17). What is span(V1, V2, V3)? Could it be all of…

A: Given vectors are v1=(-2,2,5), v2=(0,1,4),v3=(-2,4,17) we have to find span(v1,v2,v3)

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: Find u ∙ (v × w)   if u = ⟨1, 1, 1⟩ , v = ⟨2, 1, 0⟩, w = ⟨0, 0, 1⟩

A: Given: u=1,1,1, v=2,1,0, w=0,0,1 we know that scaler triple product S.T.P. of given three vectors…

Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

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Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

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Q: Compute u X v.

A: Here given vector as u=3-12, v=011 These vectors can be written as u=3i-j+2kv=j+k

Q: Let T (V₁, V2, V3) w = (4, 1, −1). = (2v1 + V2, 2v2 − 3v₁, V₁ — V3). Find T(–4,5,1) and pre-image of

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Q: Determine whether or not T = (6,-3) belongs to the null space of A' if A 1

A: the answer is

Q: Suppose W1 = span(v1, v2, v3, v4), W2 = span(v1, v2, v3, v5), W3 = span(v1, v2, v3, v4, v5) and…

A: Given: Suppose W1 = span(v1, v2, v3, v4), W2 = span(v1, v2, v3, v5), W3 = span(v1, v2, v3, v4, v5)…

Q: Express the Vector x as a linear combination of the U's U₁ Gl , 02 [1] ·16

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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Q: B. Is C a real vector space? Explain.

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (V2 - V1, V1 + V2,…

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Q: Find the projection projuv, where u = (1,3,-2) and v = (2,-1,3).

A: Since we kow that the projection of v on u is given by                projuv=u.v||u||2u

Q: 3.) Verify the Cauchy - Swhorz inequality and the triangle inequality for the vectors 3. x=(2, 0,-1)…

A: Use Cauchy-Schwarz and the triangle inequality.

Q: 1. Let V₁, V2,...,Vn be n vectors in a vector space V. Explain what it means to say that these…

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