Write x as the sum of two vectors, one in Span fu,,u2,u3} and one in Span (u4}. Assume that (u,.u4) is an orthogonal basis for R*. 2 1 4 13 - 2 -6 u, = ,u2 = , U3 = - 1 4 - 3 (Type an integer or simplified fraction for each matrix element.)

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

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

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Q: Determine whether the vectors (3,0, 3, 6), (6,0, 0, 3), (0,0,3,0),(6,3,9,12) form a basis of R*.

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Q: Answer considering the matrix with the given vectors as its columns

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Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

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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: 2 Construct a 3 by 3 nonzero matrix A so that vector is a solution to Ax = 0 -

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

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

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Q: Which one of the sets of vectors (given in Matlab notation) is linearly independent?

A: Note:  checking by matrix   if  zero vector is in the set then set is linearly independent

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: Explain  column vector of m x 1 matrix?

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Q: Find the coordinate matrix of x = (−2, 1, 3) in R3 relative to the standard basis S = {(1, 0, 0),…

A: Given: Then,

Q: Find a vector that has the same direction as [4, 2,5] but has length 35.

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Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

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: 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: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

Q: Find the change of basis matrix from B1 to B2. -1 2

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

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Q: Write x as the sum of two vectors, one in Span fu1,u2,u3 and one in Span fu4. Assume that fu1,...4is…

A: Let x = v + wWhere v = a1u1 + a2u2 + a3u4        and w = a4u4.

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: 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: Show that if C is a matrix whose columns are the components (x1, y1) and (x2, y2) of two…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: (0,0, 1), (0, 1, -1)} be a basis of R, Find the matrix for T relative to

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Q: orthonormal

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Q: Find a basis for R3 that includes the vectors (1, 0, 2) and (0, 1, 1).

A: Given vectors 1,0,2 , 0,1,1IR3 is a vector space of dimension 3 Let , the standard basis for IR3is…

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

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Q: Do the vectors {(1,–2, 1), (2, –3, 1), (5, –8, 1), (-1,1,2)} form a basis for R³? Provide a detailed…

A: ℝ3 has dimension 3. So, any basis for ℝ3 contains 3 vectors.  But the given set of vectors {(1, -2,…

Q: 1 -1] 5 -4 2 1 -3 1 -2 -1 3 2 16

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Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

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Q: stable

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Q: what is a basis? what happens when we write a vector as a linear combination of the vectors in a…

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

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Q: Define whether these vectors are linearly independent! --- u =| 2 3, 12.

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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: Find the stable vector of 1 2 4

A: The stable vector is the probability row vector w such that w*P=w Let , w= [ x  y  z ] So it becomes…

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

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Q: Find the coordinate matrix of x = (-17, 22) in R² relative to basis B' = {(-5,6), (3, –2)}. %3D %3D

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Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: Find all vectors orthogonal to 3

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Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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Q: Show that the vectors are orthogonal.

A: Given : 3,6 and 4,-2