Write x as the sum of two vectors, one in Span fu,,u2,U3} and one in Span fu4). Assume that fu. 44 is an orthogonal basis for R4. 3. 14 1 0. U2 -4 Uz = X = 1 1 (Type an integer or simplified fraction for each matrix element.)

Q: Show that in the simplex method if a variable x, leaves the basis, it cannot enter the basis in the…

A: Solution ) the simplex method is mainly focused on minimizing  the function   Let us suppose we take…

Q: 7. Use matrices to stretch the vector horizontally by a factor of 3.

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Q: Find the coordinate vector [x]gof x relative to the given basis B= {b1,., bn}. -[-]»= [-{]==(:)

A:

Q: Find a (2x2) singular matrix A that maps (2, 4) into (3, 1).

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: 2. Determine whether the vectors v, are orthonormal. If not, normalize them to produce an…

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Q: Let A be an 8 × 5 matrix of rank 3, and let b be anonzero vector in N(AT ). Show that the system Ax…

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Q: The i th row vector of a matrix product AB can be computed by multiplying A by the ith row vector of…

A: Given statement is  The i th row vector of a matrix product AB can be computed by multiplying A by…

Q: Find the stable vector of 1 2 1 3 2 3

A: ANSWER:

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

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Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: Find the coordinate matrix of x = (1, 2, −1) in R3 relative to the (nonstandard) basisB′ = {u1, u2,…

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Q: Find a basisfor the span of the given vectors.

A: Consider the provided matrix. 1-11,120,011,212 Find a basis for the span of the given vectors.

Q: Determine whether the given orthogonal set of vectors is orthonormal. If it is not, normalize the…

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Q: Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an…

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Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

Q: why cant we just multiply the 1/det(A) with the transpose of matrix like indicated in the red…

A: I am attaching image so that you understand each and every step.

Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: Find the coordinate vector of [4, -2, 1] relative to the ordered basis B= ([0, 1, 1], [2, 0, 0], [0,…

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Q: Determine whether the given orthogo­nal set of vectors is orthonormal. If it is not, normalize the…

A: Given set of vectors is

Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

A:

Q: Linear Algebra

A: According to the given information, it is required to construct an orthonormal basis of the set:

Q: Let A be annxn matrix and B=A+T, where / is the identity matrix, then it is possible for A and B to…

A: Given matrix combination is B = A + I

Q: 3 0 1 -1] -3 X= -4 -4 1 x(0) 1 1 -2 5 -1 2 16 3.

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Q: verify that the matrices and scalars in Exer- cise 1 satisfy the stated properties. (a) (AT)" = A…

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Q: orthonormal

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Q: If Pis the projection matrix onto the line through (C) (:) and then I - P projects onto the line…

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Q: 2 then the is the matrix of transition from the base B to the basis B' and the coordinates of vector…

A: Given that B and B' are bases of a vector space v and P is the matrix of transition from base B to…

Q: Determine whether the given orthogo­nal set of vectors is orthonormal. If it is not, normalize the…

A:

Q: Construct 4x4 matrix A= Lajj whose a entries satisfy Ja;;=2i ij=1, 2, 3,4 %3D

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Q: [-3 1 2]", [2 4 1]", [1 –1 2]*.

A:

Q: 5. Show that the residual vector, e, can be written as e - (I, - H)y, where H is a hat matrix.…

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the stable vector of P || -

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Q: find if the vector x is in the range for matrix A

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Q: 8. Use matrices to compress the vector vertically by a factor of X-ахis. and reflect it over the

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Q: Construct a 3 x 3 nonzero matrix A such that the vector is a solution of Ax = 0.

A: Given conditionAx = 0          .................(1)x = 111 is a solution to Ax=0,Let matrix A be - A…

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

A:

Q: (7,4) by 210 4. Use matrices to rotate the vector degrees counterclockwise about the origin.

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Q: Find change of basis matrix from ((1,2), (3,5)) to ((2,5), (3,7))

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Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Write x as the sum of two vectors, one in Span fu,,u2,u3} and one in Span (u4}. Assume that (u,.u4)…

A: Two vectors u and v is said to be orthogonal if u.v=0

Q: Does the vectors v1 = (-3, 7) and v2 = (5, 5) form a basis for R2?

A:

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: (i) Compute each Ax by dot products of the rows with the column vector: (a) 2 1 1 2 3 [10 2 1 1 2 3…

A: Since, you have asked two questions, we are attempting only the first question for now. If you want…

Q: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

A:

Q: Suppose A is a 2 × 2 matrix which rotates every vector clockwise by 45degrees . Geometrically, what…

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Q: Find the change of basis matrix from B2 to B1. B2

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Q: How many matrices are there in the vector space Mmxn(Z2)?

A: The given vector space is Mm×nZ2.

Q: 6. Compute the projections of [1, – 1,0, 1] on the vector [0, 1,0, 2]. |

A: Let v = [1, -1, 0, 1] and u = [0, 1, 0, 2]