a) matrix is a partial order: Determine whether the relation R represented by the given 1 1 01 1 MR = [a¡j] 1 1 1 1 1 %3D 1 LO 0 0 1 1.

Q: Prove that det : M2×2(F) →F is a 2-linear function of the columns of a matrix.

A: It is required to prove thatDet: M2×2(F) -> F is a 2- linear function of the columns of a…

Q: Prove that if the rows of A are linearly dependent, then so are the rows of AB.

A: Let us assume that the product AB makes sense. To prove that is if the rows of A are linearly…

Q: Let A = {1, 2, 4, 5} and B= {2, 4, 6}, and let the relation R from A to B be defined by xRy iff x <…

A: Option (b) is correct.

Q: Let f1, f2, f3 be functions in F(R). a. For a set of real numbers x1, X2, X3, let (f(x,)) be the…

A: Given that, f1,f2,f3  be the functions in F(R) It is given that fi(xj) be the 3 times 3 matrix.…

Q: Prove that if A is an m x n matrix of rank r, then the dimension of the solution space of Ax = 0 is…

A:

Q: 5. Find the three by three matrix A such that [r – y] A. y for all r, y, z in R.

A: In the given problem we have to find the three by three matrix A such that…

Q: Let A be an n X n matrix such thàt A². Show that det(A) ||

A:

Q: 10 1 Let R be the relation represented by the matrix MR and S be the relation represented by the…

A:

Q: A. Let R be a relation on set A. A={x :xeJ and 0 sx s 12), and R={(a,b) : la - b| is multiple of 4}.…

A: Since not particular question asked, as per guidelines solution to only first question(i.e A) is…

Q: A, BE R"Xn 2. Let n EN. Consider the following binary relation for A-B : 3Q E R"*": Q. A A= QB…

A:

Q: Consider the matrix 1 4 A = 2 3 (a) Compute A-1 (b) Find det(A-') (c) Deduce a relation (if it…

A: Given the matrix A = 1423 a) compute A-1 A-1=1Aadj A adj A = 3-4-21 A = 3-8 = -5…

Q: Given that p(x) ax³ + bx² + cx + d is a polynomial of degree 3 such that p(-2) = 3, %3D p(3) = 11,…

A:

Q: 6. Let B be n x n matrix. Define a function T : Mn(R) → M„(IR) by T(X) : XB – BX for all X € M, (R).…

A: A, B and C be n×n matrices, then  A(B + C) = AB + AC (B + C)A = BA + CA

Q: When A is invertible, column of A form a linear dependent set O True O False

A: When A is invertible,column of A form a linear dependent set

Q: Let R1 and R2 be the relations represented in the matrix. [0 1 0 1] [1 0 1 1] 0010 0010 R2 1 100 1 1…

A:

Q: Determine whether the relations represented by the zero-one matrix are equivalent and explain your…

A: We are entitled to solve only one question at a time, so we will answer only the first question.…

Q: VII.3. Let Rbe the relation on {1, 2, 3, 4} given by r Ry if, and only if, æ – y = 0. Represent Rin…

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Q: Г2 1 Let T : R3 → R² be the linear map corresponding to the standard matrix Compute 1 3 T O A. 8 O…

A:

Q: Let R1 and R2 be relations on a set A represented by the matrices below: MR1 0 1 0 1 1 1 1 0 0 Mr2 =…

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Q: 10 - Which of the following matrix represents the symmetric closure of R? (1 0 1 0\ 0 1 0 0 0 0 1 1…

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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: Suppose T: R – R2 and S: R² → R3 are the linear maps defined by a - b x + 3 y a and S a + b -a + b 7…

A:

Q: Let R,and R2 be relations on a set A represented by the matrices Mg, =10 0 0 1 ol and MR2 1 0 Find…

A: In this question, we have to find the product and composition of the relation matrix. To find the…

Q: Let L be the operator on P3 defined byL (p(x)) = xp'(x) + p''(x) Find the matrix A representing L…

A: L (p(x)) = xp'(x) + p''(x) We have to find the matrix A representing L with respect to [1, x, x2].

Q: Let A and B two matrices of order n x n. Prove the follwoing claims: (a) N(A)NN(B) CN(A+ B). (b)…

A:

Q: Let R1 and R2 be the relations represented in the matrix. 1001 11 1 1 1 1 1 11 0 1 0 0 0 1 1 0 1 0…

A:

Q: How can the matrix for R-1, the inverse of the relation R, be found from the matrix representing R,…

A: ANSWER :

Q: Let P be an m × m matrix with entries in the polynomial algebra F [x]. L:1.1.

A:

Q: 1. By using the attached graph of relation R1.  a) Express R1 as a set of ordered pairs. b) create a…

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Q: Let X be a set of 2×3 matrices. if for any a1 az az A = B = b1 b2 b3 b4 b5 b6 EX, a4 a5 a6 6 d(A, B)…

A:

Q: Let R1 and R2 be relations on a set A represented by the matrices below: MR1 = 0 1 0 1 1 1 1 0 0 Mr2…

A:

Q: Let R1 and R2 be the relations represented in the matrix. 111 1 100 1 0 1 1 1 11 0 0 0 1 1 0 1 0 R1…

A:

Q: Construct the dual of the following Convex optimization Hinimize IJ Ay-bu Subject to Qx =P full rank…

A: Given, Minimize Ax-b22Subject to,                   Qx=P And A and Q are m×n and p×n full rank…

Q: Prove: For all m,n E N, (A†)™ = (A")† holds for all m x n matrices A.

A: Given that m,n∈ℕ. Let A be an m×n matrix. Let A+=Z. We know that A+=Z is pseudo inverse of A if it…

Q: Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0) 1 0 0 1 1 0…

A: The set is A = {a, b, c, d}. The matrices representing the relations R and S, respectively, are as…

Q: Let Mı5(IR) = {A/A and 15th order square matrix with real elements} and consider the linear…

A:

Q: 17.Consider the linear system dxdt=a11x+a12y,dydt=a21x+a22y,dxdt=a11x+a12y,dydt=a21x+a22y, where…

A:

Q: Let A be an m x n matrix. Is the set K defined below convex ? Why or why not ? K = {y € R" : 3r E R"…

A:

Q: Let R be a relation on A = {1,2,3,4} such that aRb means |a – b| < 1. Find the matrix…

A:

Q: Given the following matrix representation of a relation R on the set A = {a, b, c, d}, which of the…

A:

Q: Let A = {2, 3, 4, 5, 6}, B = {11, 12, 13, 14, 15} and define the relation R from A to B by aRb if…

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Q: Exercise 1 find the relation Ship between PeSIstarce IC furrent) from the table below, VAR 1 2-28 10…

A: Given that  R V I 2 1.2 0.6 4 1.42 0.355 6 1.61 0.268 8 1.83 0.229 10 2.10 0.219 12…

Q: List the ordered pairs in the relations on {1,2,3} corresponding to the matrix, [1 0 = 10 1 1 11 1.

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Q: Let R1 and R2 be the relations represented in the matrix. [01 0 1 [1011] 0 010 0010 0 R2 1 100 1100…

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Q: Matrix A is equivalent to matrix B, written A B, if there exist nonsingular matrices P and Q such…

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Q: Consider B={1,x,x^2} and B'={1+x,1-x^2,2} Find the change of basis matrix 1.P from Bto B' 2.Q from…

A: Given bases are B=1,x,x2, B'=1+x, 1-x2, 2 let B'=b1, b2, b3 So change of basis matrix from B to B'…

Q: 5. Let A be an m x n matrix and define F: R" → R"m by F(r) = Ar. (i) Prove that there exists C > 0…

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Q: Let R1 and R2 be relations on a set A represented by the matrices below: Mr1 = 1 1 1 1 1 0 0 Mr2 = 0…

A: Given:

Q: Consider A = -1 and D = Given that there exists an invertible matrix P such that D = P-1 AP,find…

A: Given A=22-15For eigenvalues|A-xI|=0(2-x)(5-x)+2=010+x2-7x+2=0x2-7x+12=0(x-4)(x-3)=0x=4,3 are the…