Take the function on the vector space R3. = 3xıyı+4x2yz+x3y3 Where x = (x1, X2, X3) y = (yı, y2, y3) The given function defines an inner product on R3. 1. Express how , show one basis for it.

Q: If B is the standard basis of the space P3 of polynomials, then let B = {1,t,t,tº). Use coordinate…

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

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Q: If Apq is a symmetric tensor, Bpq is an anti-symmetric tensor, then prove that ApqBpq = 0

A: Given two tensors Apq & Bpq such that Apq is symmetric and Bpq is anti-symmetric. To prove that…

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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…

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Q: Define the term Change of basis?

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Q: a. Write the solution set to the following equation in parametric vector form (consider ₁ to be the…

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Q: Explain the term Vectors that Span a Subspace.

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Q: A basis of {(a, b, c, d) : b = 6c + d, a = 0} (A) {(0,0, 1, 0), (0, 6, 0, 0), (0, 0, 0, 1), (0, 1,…

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Q: Find the basis for the orthogonal complement V: v1=(1,-3,3,5) v2=(2,-5,9,3)

A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

Q: A basis of {(a, b, c, d) : b = 6c+ d, a = 0} (A) {(0,0,1,0), (0, 6, 0, 0), (0, 0, 0, 1), (0, 1, 0,…

A: We have to check

Q: Write a second degree equation matrix and prove that it is in vector space?

A: To show: An example of a second-degree equation matrix which is in vector space.

Q: Explain why S is not a basis for R2. S = {(4, 3), (12, 9)} S is linearly dependent. O s does not…

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Q: Basis Find a basis for the space of 2 x 2 lower triangular matrices.

A: In this question, we have to find the basis for the space of 2×2 lower triangular matrices. We know…

Q: need help on this question   given the basis B={[12],[25]} of R2.{"version":"1.1","math":"\mbox…

A: We have to find the change of coordinates matrix from the standard basisE=1,0,0,1 of ℝ2 to the basis…

Q: If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², 13³). Use…

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Q: Find a basis of the subspace of R³ defined by the equation 2x1 + 3x2 + x3 = 0.

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Q: How do you find a basis for a given subspace? May you please throw in an example too?

A: See the attachment.

Q: Determine whether vectors (-1,0,1,2),(1,0,-3,0),(1,0,0,0),(1,5,-1,-2) from the basis for R^4 Please…

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Q: The vectors (attached) form a basis of R^3 (R = Real numbers) if and only if k does not equal blank

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Q: Find a basis of the subspace of R* consisting of all vectors of the form X1 -8x1 + x2 —6х — 2х2 -6x1…

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Q: (a) (b) A = 1 0 1 1 2 -21 ∙1 -3 5 Find the basis of N(AT)¹ and C(A)-. Let a be the basis of N(A),…

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: Determine the following three vectors {, , } forms a basis for R^3. Expalain your answer.

A: Answer  Given  <2,1,0> , <4,2,2> and <-2,-1,3>  Let check whether they are…

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Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

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Q: Check whether the set V= {(2, 3), (3, 4)} is basis of R2 or  not?

A: this a spanning set and linearly independent so the vectors forms a basis of R^2

Q: Any given vector space may have distinct inner products.  True  False.

A: Given :- Any given vector space may have distinct inner products. To find :- The given statement is…

Q: A basis of {(a, b, c, d) : d = 2a + b, c = 0} (A) {(1,0,0, 2), (0, 1, 0, 1)} (B) {(2,0,0, 1), (0, 1,…

A: The objective is to find a basis.

Q: Find all possible real numbers a, b, c, d E R such that form a basis B= (v.w) for R² that satisfies…

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