x · y = (x + y² – x² - y²)

Q: Let u and v be non-zero vectors in 3-space. Prove that u and v are perpendicular if and only if |u…

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Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

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Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: Let v1 and v2 be vectors in an inner product space V.(a) Is it possible for |{v1, v2} | to be…

A: It is given that,  v1, v2 be the vectors in an inner product space V. a) We have to determine that…

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

Q: In a vector space V, prove that (-1)v= -v for all v E V.

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Q: Show that the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).…

A: An inner product on real spaces V is a function that associates a number u, v with each pairs of…

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: If A is diagonalizable then A´is diagonalizable. Select one: O True False

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Q: Please go through each option with explanation

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Q: Find the Euclidean norm for vector v = [2 3 1 -1]

A: We have to find the euclidean norm

Q: Let v1 =[1,4,-2] , v2 =[-2,-3,7] , b =[4,1,h] FIND all value(s) h such that b is in span{v1 , v2 }

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Q: Let U(-5, -4, 3, 4, 6), V(-4, 1, 7, 1, 0). Find the inner product U.V

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Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Let u be a linear combination of {1₁, 1₂, 13). Select the best statement. A. span{u₁, U₂, U3} =…

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Q: True/False: If A is diagonalizable, then so is AT.

A: A matrix is said to be diagonalizable if a matrix of n×n elements has n linear independent eigen…

Q: The usual absolute value on the real numbers is a vector norm. Select one: True False

A: solution of the given problem is below...

Q: Prove the following relation in the vector triple product : Ax(BxC) + Bx(CxA)+Cx(A x B) = 0

A: The answer is given in handwritten form in the step-2 box. Please check it.

Q: A Show that the function f: R² → R defined by f(x₁, x₂) = x² + 2x² + 3x₁x₂ + 4x₁ + 5x₂ + 6 is a…

A: Definition of Vector Quadratic Function : Given Function f: R2→R is a vector quadratic function if…

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Let x(bar) = (3,-5,2,1,-2) element of R5. Find the norm of x(bar) using the usual norm on R5

A: The norm of x is the distance between a point x to the origin.

Q: If {v1, V2, V3} is an orthogonal set of nonzero vectors in an inner product space V, then prov that…

A: This question is related to linear algebra (inner product space).

Q: Given n=7. Then only one method of the following can be used to approximate a definite integral:…

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Q: Find the norm of i and the unit vector i in the direction of a if ||7|| =

A: Solutions

Q: Find the norm of a and the unit vector ū in the direction of a if -5 -3 1 -2 |||| i = ||

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Q: . Let C and D be convex cones in a vector space. Show that Cn D and C+ D are convex cones.

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Q: Give an example of a norm space.

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Q: Let W be the set of all 1st degree polynomials (or less) such that p-p^2. Which statement is TRUE…

A: Given W the set of all ist degree polynomials such that           p=p2  Let p= 1  ⇒12= 1  Thus p=p2…

Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.