4. Apply the principal axis transformation to the curve of second order -x2 + 6xy – y? – 22.x+ 18y – 31 = 0. Construct the orthonormed basis which belongs to the transformed coordinates and determine the type of the curve. Second test

Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

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Q: Let b = (2, -4, 2). Let W be the hyperplane b-. (a) What is the dimension of W? (b) Find a basis for…

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Q: Explain why S is not a basis for R2.S = {(−3, 2)}

A: We know the definition of basis, let V be a vector space. Let B be a set of vectors in vector space…

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: 5. W is spanned by the vectors 24 -3 9 and Find a basis for W¹.

A: The basis for W is:Basis of W= 24-3-8 ,  -1-225

Q: Let B = 3 (1, x + 8, (x − 1)², 2x³) be an ordered basis for P3. Find the coordinate vector of 3 -…

A: fB​=[161, −19, −6, 4]Explanation:Detailed explanation:This is a detailed guide explaining how to…

Q: Q3. a) Express the vector (4,2) e R' as linear combination of the vectors (1,1) and (1,-1). b) Let T…

A: We have to find all these

Q: Find a basis of the subspace of R4 defined by the equation -9x1 - 5x2+6x3-7x4=0. Basis:

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: . Determine if the vectors (3,2,0) , (-3,0,1) , and (1,1,–9) span all of R’ . Do these vectors form…

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Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. 2 pan{ [ ² ]- [8]} 6 S = span (8)

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Q: The set B = {1+t², t + t², 1 + 2t + t²} is a basis for P₂. Find the coordinate vector of p(t) = 1 +…

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Q: - Let B = {v1, V2, V3} be the ordered basis of R3 consisting of V1 = 1 V2 = - V3 = 1 Find the…

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Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: 5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1),…

A: we will find the coordinate vector with respect to the given basis.

Q: 6. Let B be the following ordered basis for R?: в %3 {(1,—1), (2, -3)} . Find the coordinate vector…

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Q: 3. Let L: R* → R³ be defined by U1 U1 1 1 1 U2 U2 1 2 1 Let S and T be the natural L U3 U3 1 -2 1 U4…

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Q: 2. Find a basis for the set of vectors in R2 on the line y = 5x.

A: Now here,

Q: Let T : R → R³ be a linear dS be the sta [2 0 2] AT 37 1 2 5 4 S+S B = {(1,0, 1), (2, 0, 0), (0, 1,…

A: we are given standard matrix of T and v as coordinate vector with respect to basis B we need to find…

Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

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Q: The vectors 02 = 6. 03 = form a basis for R' if and only if k +

A: Given vectors are: v1→=4-10,v2→=-666,v3→=24k We have to find the value of k when the vectors form…