sider the ordered bases B= ((4, –9), (–3,7)) and C = ((4,3), (–2,4)) for the vector space R’ %3D

Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: Write the vector w = (1, 1, 1) as a linear combination of vectors in the set S. V2 V3 S = {(1, 2,…

A: See the attachment.

Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Suppose that the vectors [1, –3, 1] and [2, 4, –1] form the sides of a parallelogram. Find the…

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Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

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Q: If ū = 2î – î and w = î + 2ĵ, find the compo- nent form of V = ũ + w and sketch the specified vector…

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Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: In R³ you are given the vectors a = (21,-9, -21,-4) b = (x, -35, -16, -23) Choose a such that b…

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Q: Multiply the matrix P = A(ATA)-¹AT by itself. Cancel to prove that P² = P. Explain why P(Pb) always…

A: Here the Matrix . For this matrix P, .

Q: Which of the following statements is not true for vectors a, b and c and scalars a and B (A) a.b+a.c…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: 1 (a) Write the following vectors as column vectors. i. 4e₁-3e3 +22₂ - 2e₁ € R³. ii. e₂ + ₁ - 52₂ €…

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