For a given k, 1 ≤ k ≤n, how many vectors (x1, x2,. , xk) are there for which each xi is a positive integer such that 1≤x1

Q: Determine whether the set in P_2 is linearly independent.    S={x^2 , +1, 2 - 1, 2}

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Q: Let 71, 72, 73 be any vectors in a 3-dimensional space. Determine whether the following statements…

A: You have put multiple questions without any numbering. So, according to the guidelines, we solve…

Q: 10. Let n > 2 be an integer and let V be the subset of F" consisting of vectors (x1,..., xn)…

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Q: Given that {an, 92, 93, any is a linearly independent set of vectors in a Vector space • V'( note…

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Q: - c(13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18) Fine the vector y by the…

A: year x 1951 13 1952 23 1953 21 1954 27 1955 37 1956 52 1957 34 1958 42 1959 31…

Q: Let u =(5,5,0) and v=(,5,5,(5sqrt2). Compute |u*v|

A: Approach to solving the question: Detailed explanation: Examples: Key…

Q: find the rank, nullity, row space & null space of the ff: A = [1, 5, 3, 2 0, 4, 2, 1 0, 8, 4, 5 1,…

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Q: Find u, u = (-1, 4), v = (4, 5) (a) ||u|| v, uv, and d(u, v). (b) ||v|| (c) (d) U V d(u, v)

A: The given vectors u=-1, 4, v=4, 5. We have to find the values of u, v, u.v, du, v.

Q: use Gauss Fordanmetrecd to Solbe the fellowsing setafeg Qe linear 2X+ -4x2 +6X3=5 A +3X2-783=; + 5…

A: Introduction: A system of linear equations can be solved using Gauss-Jordan elimination method. This…

Q: Determine whether w is in the column space of A, the null space of A, or both. 3 7 5 -6 3 1 A = 0 -4…

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Q: a Let A = b - a then A is diagonalizable. b Select one: O True O False

A: Use the results and roperties of diagonalization of matrix to solve this problem.

Q: Let vị = V2 = V3 V4 and -[1} Confirm that p = V1 +v2 + ¿v3 + ¿V4 and vị – V2 + V3 – V4 = 0. Jse the…

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Q: * Find the Cartesion Coordinates of the points. (),(万,). (-2,2)

A: To convert Polar coordinates r, θ to Cartesian coordinates x, y apply:x=rcosθ   y=rsinθ

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: Let 7 -7 2 -2 -5 %3D - 3 -2 9. -8 a) Find the dimension of the row space ofA. b) Find the dimension…

A: The given matrix,A=117-72-2-565-3-25409-8

Q: Verif the Caudy-Schwarz inequality and the triangle inequality 4.) for the vectors. (3,8,4,1) 4₁ X =…

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Q: 5- Suppose that A = {x1 = (3,1,2), x2 = (0,0,2), x3 = (2,0,1)} then [A] = R³, that means for every…

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Q: fx and y are two n-vectors, then prove that 1 1 -+-=1 (Holder inequality) (b) xy, <,, (Schwarz…

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Q: Let A € Rmxn and suppose that the rank of A is m where m is less than or equal to n and be Rm.…

A: Given: We are given a matrix A of size m×n with rank m where m≤n, a vector b of length m×1, and a…

Q: Compute u – 3v, u v and u x w.

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Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

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: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: Create a vector a with elements = (-1)" 2n (2n)! 1≤n≤ 100

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Q: Q7) True or False, and Justify your answer. If v1, v2, ... V4 are in Rª and v3 = 2v1 + v2, then…

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Q: = If w₁, W2, W3 are independent vectors, are the sums V₁ = W2+W3 and V₂ W₁ +W2 independent or…

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Q: (-4,2+i, 1), and y = (i, 5, 1 + i) be vectors in C. Compute (r, y), Let z = ||x||, ||y||, and ||r+…

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Q: Suppose that u₁ and u2 are vectors with ||u₁|| = 2 and ||u2|| = 3. You are also given that u₁ · U₂ =…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…

Q: Find the vector determined by 18 || = B = {[.]. 9 6 12 3 9 2 -8 " where B = 3 [-]

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Q: Prove that in P2 (the set of all polynomials with degree n< 2), every set with more than three…

A: Linearly dependent set:  A set of vectors α1, α2,α3, … ,αn is said to be linearly dependent if ∃ c1,…