Compute the Banzhaf power indices of A, B, C, and D in the systems [5 : 4, 2, 2, 1] , [10 : 7, 5, 4, 2], [4 : 3, 2, 1, 1], and [10 : 8, 7, 4, 2].

Q: Explain whether S = {1, 2x, x -4, 5x} is a basis for P2 or not

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Q: 7. Which of the following is the LU decomposition of 4 -2 3? 8. -2 1 0 2 1 -2 2 1/2 2 -2 1 -4 1 2,…

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Q: Write down a set S of matrices such that every square matrix whose characteristic polynomial splits…

A: We know that, If A is n×n square Matrix then Jordan Canonical Form(JCF) of A  is similar to A. Let S…

Q: Let A be an m × n matrix. Prove that rank(A) ≤ min(m, n)

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Q: Consider a 3 by 3 matrix A, where a11, 022, 933 are all zero. Suppose |A|0, how many terms in the…

A: Follow the procedure given below.

Q: 31. If A and B are n x n matrices, then the diagonal entries of the product matrix AB are…

A: Matrix multiplication is possible only when the number of columns of first matrix are equal to the…

Q: 10. Suppose that A is an n x n matrix with real entries such that the diagonal elements are all…

A: The problems with proof can be solved by using the concepts in linear algebra. A diagonally dominant…

Q: Every basis for R4 contains

A: Every basis of ℝ4 contains ______________

Q: Prove that if two rows (columns) of the n × n matrix A are proportional, then det(A) = 0.

A: Consider the n×n matrix A whose two rows consider R1 and R2 are proportional.…

Q: Explain why S is not a basis for M22

A: We have t.o show that why S is not Basis for M2,2: Concept: The dimension of a vector space V, is…

Q: Let S be a set of four vectors in R* with the property that every subset of S consisting of three…

A: The solution are next step

Q: Suppose that B and C are ordered bases of R. Find the conversion matrix from B to C.

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Q: 5. Which matrix is skew symmetric? O A - AT O A +AT O AAT O ATA

A: We have to find which matrix is skew symmetric.

Q: Let Q be the n × n real matrix in which each entry is 1. Show that det(Q−nIn ) = 0.

A: Given:         Q=11....111....1....................11....1n×n,…

Q: Let A be an n ×n matrix. Prove that dim(span({In,A,A2, . . .})) ≤n.

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Q: What scaling matrix S (in homogeneous coordinates, so 3 by 3) would produce a 1 by 1 square page…

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Q: Consider the matrices shown below: A [閒 Compute tr((CTB)AT) 25

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Q: Let the rows of A ∈ Mn×n(F) be a1, a2, . . . , an, and let B be the matrix in which the rows are an,…

A: This can be done as follows:

Q: 7. For which integers n, there is a Hadamard matrix of order n?

A: The order of an Hadamard matrix is 1,2 or 4t,where t is an natural number . So,n=1,2 or 4t.

Q: 4. Prove that a permutation matrix is orthogonal. 5. Let A = -1

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Q: Find a 3 x 3 matrix A such that Az = 10 for all i in R³. A =

A: Given Ax=10x  We have to find 3×3 matrix A  Now

Q: Let n >1 and let D be an alternating (n- 1)-lincar functic matrices over K. For each j, 1 sisn, the…

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Q: Show that if A is skew symmetric, then the elements on the main diagonal of A are all zero.

A: given that A is skew symmetric

Q: 13. Find an estimate for det (A) if A is an n × n matrix whose entries form some pattern of +10's

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Q: Determine whether S = {1– x, 2x - 3x2,x2 - 2x3,2 + x3} is a basis for P3

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Q: The matrix that implements the mapping T (₁, 2) = (-3x1 +4x2,0, 7x2 - 5x1,1 + 2x₂) is -3071 4 052 0…

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Q: Find A and a- basis for which the system reduces to ú: lu+ v and i = av

A: We have to find the value of λ and a basis for which the system reduces to  u·=λu+vv·=λv

Q: Let M and N be 3 x 3 matrices with det(M) = 64 and det (N) = 81. Calculate det Also show whether NT…

A: Let M and N be are 3×3 Matrices. We have given that ,  detM = 64  and  detN = 81 We need to find ,…

Q: (c) Find a basis for the row space of A.

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Q: (1) Suppose the last column of AB consists of all O's but B itself has no column of zeros. Are the…

A: as you are asking multiple questions I have solved first one , please repost with the remaining…

Q: Compute the consistency ratio of the following matrix. 51 2 1 2 A = 0.5 1 L0.2 0.5 1- Answer:

A: Consider the given matrix A=1250.5120.20.51

Q: Use the matrix C to find C-1. -5 6 3 2 -2 1 9 7 -12 4 C= 12 2 -7 10 10 3 2 8 7 -4 1 3 9. 23 C-1…

A: Given The given matrix is C=-5632-2197-124122-710103287-4139232

Q: 18. W is the set of all matrices in M,, such that A² = A. %3D n,n

A: W is a vector subspace of vector space V iff W is closed under vector addition and scalar…

Q: For any two kn-matrices A a

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Q: 4. (a) Use the Gram-Schmidt process on the basis {(1,2,3), (1, 1, 2), (2, 3, 1)} to find an…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Consider the bases B1 = {(1,2), (- 3,0)} and B2 = {(3,2), (- 1, –2)} of R. The input to "(2.1)' of…

A: Consider the given vectors. B1=1,2,-3,0B2=3,2,-1,-2 Express the vectors in linear combination.…

Q: 2) Determine whether S = {(0,3,-2), (4,0,3)(-8,15, -16)} is a basis for R3.

A: Given that, S=(0,3,-2),(4,0,3),(-8,15,-16)

Q: Find a basis for the subspace of R4 spanned by S. S = {(3, 9, -3, 53), (-5, 3, 5, -3), (8, -5, -8,…

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Q: show that if √a+√b ≠ 0, then ℚ(√a+√b ) = ℚ(√a,√b ) for all a and b in ℚ. [Hint: Compute (a - b) /…

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Q: 4. Find the values of w, x, y, and z using Gauss-Jordan Elimination 1 5 -2| 7 3 2 0 |12 2 -2 0 3 5…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: Let A be an m × n matrix. Show that N(ATA) = N(A).

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Q: Consider the following basis of R5 B = {(1, 0, 0, 0, 3),(2, 2, 6, 0, 0),(0, 0, 0, 0, 1),(0, 4, 0,…

A: Solution of the problem as follows

Q: Find a basis for R³ including as many columns of A as possible.

A: First we will find the column space of A and then we will extend the column space of A into the…

Q: A matrix Q ϵ Mnxn(R ) is called orthogonal if QQt = I . Prove that if Q is orthogonal, then det(Q) =…

A: Given data: The orthogonal matrix is given by "Q". The given condition is  QQT = I.....(1) Now, take…

Q: 2 Find a basis for the column space of A = 9. 7 -5 {[ 2 Ex: 5 Ex: 5 -5

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Q: Find a basis for Q(3^(1/3), 3^(1/2)) over Q.

A: It is known that,

Q: Tawing questions

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Q: п> 2, пeN , let For every A, B,C, DeMn matrices AC – BD = IņandAD det(AC) > 0

A: Given: For every n>2, n ∈ N A,B,C,D be square matrixes A,B,C,D AC-BD= In---- (1) AD+BC= On----(2)…