16, The set of all upper triangular n x n matrices is a subspace W of Mnxn(F) (see Exercise 12 of Section 1.3). Find a basis for W. What is the dimension of W? 12. An m x n matrix A is called upper triangular if all entries lying below the diagonal entries are zero, that is, if Aij that the upper triangular matrices form a subspace of Mmxn(F). = 0 whenever i > j. Prove

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A: The given set is a11b | a, b∈K. It is known that any subspace should contain the identity element.

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A: Answer (6)  Suppose that A is an n × m matrix of rank 3 , the nullity of A is 3 , and the column…

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Q: 12. B' = (1 + x − 2x², 3+2x + x² − 2x³,2+x+3x² − 2x³). -

A: 12. Given B'=1+x-2x2, 3+2x+x2-2x3, 2+x+3x2-2x3   Also, set S=a0+a1x+a2x2+a3x3∈ℝ3x : a0+a1+a2+3a3=0…

Q: §5.1, Exercise 17. For which scalars a, b, c do the solutions to the equation ax + by = c form a…

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Q: 5. (а) Show that the formula ((: :) (; 3)) = xã + 2yỹ+ zž + 2wũ gives M2x2(R) the structure of an…

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Q: Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}

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Q: [1 Let matric A be a square hermitian matrix= |2 4 5 5 1. L3 Use Gram-Schmidt process to find the…

A: Consider the given matrix, A=123235351 Let u1=123, u2=231, u3=351 Step 1: u1=v1 v1=123 Step 2:…

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Q: Let S be the subspace of R4 spanned by x1 = (1, 0,−2, 1)T and x2 = (0, 1, 3,−2)T . Find a basis for…

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Q: 7. Consider the ordered bases B = (sin(3x), cos(3x), sin (3x), cos (3x), sin(3x) cos(3x)) and C =…

A: For the solution of the problem follow the next steps.

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Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 4, 7), (-1, 5, 7), (2, 5, 1)}

A: The matrix form the vectors is: A=1-12455771

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Q: Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}

A: To find the basis for the subspace of R3 spanned by the given set of vectors S.

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Q: 7. The set of all 2 x 2 upper triangular matrices is a subspace of M22- a. True. b. False.

A: Use two step test of subspace to solve this problem.

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A: Let S=3, 1, 1, 3, -2, -1, -1, -3, 4, 2, 1, 3, -12, -6, -3, -8

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Q: 4. Let Mag, denote the set of all n x n magic squares, and let Mag, denote the set of all n xn magic…

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Q: Find a basis for the subspace of R³ spanned by S. S= {(4,2,-1), (1,2,8), (0,1,2)}

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A: 4.1) let W be the set of all matrices that satisfies A12-11T=AT12-11T. To Prove: W forms a subspace…

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Q: Find a basis for the subspace of Rª spanned by S. S = {(2, 5, –3, –5), (-2, –3, 2, –2), (1, 3, –2,…

A: This question related to linear algebra's topic basis of vector space.

Q: Let A be a 4x4 singular matrix. What is the smallest possible dimension of Null Space of A? A) 2

A: Using,  Rank- Nullity Thereom

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Q: 1. For each matrix A, find the singular value decomposition in the matrix form A UEVT T-3 117 [3 7 1…

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Q: Please see image

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Q: The set of all nxn matrices having trace equal to zero. is a subspace W of Mnxn(F). Find a basis for…

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Q: 4. Consider the subspace V of R' given by 1 3 V = span (a) Find an orthonormal basis for the…

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Q: Let A e Mnxn and W be the set of all solutions for the homogenous linear system AX = 0. Prove or…

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