Let W be the set of all vectors of the form [3s 4r5t] 2r + 2s - t 3s - r + 5t 3r+2s + 4t with r, s and t real. Find a matrix A such that W = im(A). A = Let A = A basis for the image of A is -9 -6 9 3 8 -6 -8 -14 -11 4 11 15 Find a basis for the image of A (or, equivalently, for the linear transformation T(x) = Ax).

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A: A vector belongs to the column space of matrix if the vector can be expressed as a linear…

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Q: Let a € R, and define vectors u₁, U2, U3 € R³ in terms of a by E] 2 U₂ = a U₁ = 3a +3 2a +3 a² + 3a]…

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Q: Let A be a 6 × 5 matrix with linearly independent column vectors a1, a2, a3 and whose remaining…

A: (a) it is given that A be a 6×5 matrix with the columns a1, a2, a3, a4, a5 and a4=a1+3a2+a3,…

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A: Given below the detailed solution.

Q: Q2) In each of the following cases, find the matrix A for which [v]D=A[v]B a. B={1, 2x, 4x²-1} and…

A: Here we use the definition of the change of basis matrix. For that we first write the basis elements…

Q: Let W be the set of all vectors of the form with r, s and t real. Find a matrix A such that W =…

A: To find matrix A such that

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A: Given thatWe have to approximate Projwu and Projuw.We know that

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A: as we know that when a matrix is multiplied by a vector then the product is a vector.

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Q: Let W be the set of all vectors of the form [3s 4r5t] 2r + 2s - t 3s - r + 5t 3r + 2s + 4t with r, s…

A: The set ( W ) consists of vectors that can be formed by linear combinations of the vectors with…

Q: Perform the elementary row operation R2 → R3 to matrix B to obtain matrix C. -1 0 0 01 1 2 4 2 -2 A…

A: Our Aim is to perform the elementary row operations R2↔R3 to the matrix given below:-

Q: 2. Diagonalize the matrix using normalized vectors. B= 3 1

A: Given,        B=1331

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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 Data: The given details are We want to create a matrix that reflects around a line that is…

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A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

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Q: 4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]

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Q: -3 -3 9. 2 Let A = -3 -6 12 and b = 3 -3 -2 13 -5 Denote the columns of A by a1, a2, a3, and let W =…

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Q: Let W be the set of all vectors of the form with r, s and t real. Find a matrix A such that W =…

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Q: a4 a1 Let V1 (3).. b4 be four vectors in R³. b₁ b₂ V3 = C1 C2 C4 a1 a2 a3 a4 If we reduce the matrix…

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Q: be the set of all vectors of the form 4r – 6s – 6t | r + 3s – 15t - 11r + 7s + 8t 14r + 11s 6t with…

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Q: entries

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