Consider the matrix mapping A:Rº→R³ where 1 0 4 0 0 2 1 3 1 2 4 0 0 A = 200 2 0 Sub-Task (1). Find a basis and the dimension and the dimension ( Sub-Task (2). Find a basis Sub-Task (3). Find each column Ck (k=1, 2, 6) of A that is a linear combination of preceding columns. Explain your answer. No justification-no points. ... of the KerA. .) of the ImA. 1

Q: Let the set {v,, v2} be linearly dependent. Determine whether the set {v, + 4v,, 5v, - v2} is also…

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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 a basis for the column space of the matrix. (Enter each vector in the form [x, x2, J. Enter the…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

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Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: If a and b are integers, then a/b is always a rational number. True False

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Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = (0.375,…

A: Given: In this problem, the given details are We want to create a matrix that reflects around a line…

Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(−5, 6), (3, −2)}, x = (−17,…

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Q: The set is a basis for R2. Find the coordinates of the vector [x] B = = -16 11 B -6 = -{[1].[:]}…

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Q: Find a basis for the null space of the matrix A = -10 25 5 -6 15 3 2 -5 -1 LO Enter your basis…

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Q: Let A = {a₁,a2,a3} and B = {b₁,b2,b3} be bases for a vector space V, and suppose a₁ = 4b₁ b₂, a₂ = −…

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Q: For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. A = 3 2 - 12…

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Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = { (9, −3, 15, 4), (−3, 0, 0,…

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Q: 6. An n x n matrix A is diagonalizable if and only if it has n distinct eigenvalues. ? 7. Let W be a…

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Q: Let A= {a,,a2,a3} and B= {b,.b2.b3} be bases for a vector space V, and suppose b, = 5a, - 3a3, b2 =…

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Q: Let: v = the matrix: -20 -15 11 18 Write v as a linear combination of the vectors in the following…

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

A: The given vectors are 1110,  1101,  1011   and 0111. Consider the matrix A=1110110110110111.

Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(8, 11, 0), (7, 0, 10), (1, 4,…

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Q: For the matrix A, find an orthogonal matrix P such that P-1 A Pis diagonal. 3-2 41 A = I ده است مراد…

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Q: For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 3 2 - 5 - 4 A…

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Q: Orthogonally diagonalize the matrix. A = PDPT, where P A = 2 0 0 0 1 -1 and D 0 −1 1

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Q: Find the coordinate matrix of x in Rn relative to the standard basis.x = (−6, 12, −4, 9, −8)

A: The given vector is x =  (−6, 12, −4, 9, −8).One has to find the coordinate matrix of x relative to…

Q: - 3 HG 4 4 5 1 2 Let P = - 3 1 3 - 1 W₁ = -5 0 - 4₂ = a. Find a basis (U₁, U₂, U3} for R³ such that…

A: (a)It is given that, P is the change of coordinates matrix from to .Also, the values are:So, using…

Q: Find the vector x determined by the coordinate vector ---(DBE) 8 and the basis B = 0 XB = The vector…

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Q: 7. For the matrix: A = b. B Row B Rank (A)= -4 a. Find a basis for the row space of A and rank(A). 1…

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Q: Find an orthogonal basis of the column space of the following matrix: 1 -5 6 4 -1 A = -4 -1 -13 9 2…

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Q: 5. Consider the vectors u 11. and y= a. Use row operations on an augmented coefficient matrix to…

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Q: 2 3 For A = 0 -1 0 orthogonal matrix Q. V₁ = Ex: 5 1 -2, find the orthogonal vectors V₁, V2 and V3…

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Q: []B = Find the coordinate vector of = 2 4 with respect to the basis B = [1] 0 {CC)6]} 2 for R³.

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Q: Explain why S is not a basis for R2. S = {(-6, 6)} O sis linearly dependent. S does not span R². S…

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Q: For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 3 2 -2 -4 A=…

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Q: Determine the change of coordinate matrix from the given ordered basis ? to the given ordered basis…

A: Given: Given ordered basis for ℝ2 is X=-5,-3,4,28Y=6,2,1,-1 we want to find change of coordinate…

Q: et B = and C = {c1,c2} be bases for a vector space V, and suppose b, = 8c, - 5c2 and b2 = - 7c, +…

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Q: Define 0 1 B. - 13 V3 = 0 (Here, a, b, c, d are some unknown constants.) Assume that v3 is nonzero…

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Q: Consider the matrix A == ((1, 2, 5)|(4, 6, 7)|(1, 5, 1)) and the row vector v = > A = ((1, 2, 5)|…

A: As per guidelines, I can do only first question (Question 1.)