1 Let B, A Square matrixes of the same order. i. Prove that the matrix AB' + BA' İs symmetrical ii. Suppose that A is symmetric, and B is antisymmetric i.e., B holds B' =-B Prove that the D= A° B - BA° matrix is symmetric

Q: a) Prove the following: a+b a a a+b =b° (3a +b) a a a a+b

A: Since you have posted more than one question, we solve the first one for you. For the other…

Q: Consider the matrix 19 19 A = 19 10A° = 5XT + I2, When solving the matrix equation , the matrix X…

A:

Q: Let Eki be the elementary matrix formed by subtractingα times the ith row of the identity matrixfrom…

A:

Q: Define nullspace.

A: We have to define, what is null space.

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

A:

Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

A:

Q: Let A = Diagonalise this matrix. That is, find a diagonal matrix D and an invertible matrix Q such…

A:

Q: A) Justify if the matrix A is diagonalizable.B) Find a matrix T and a diagonal matrix J, such that…

A:

Q: Find the specified change-of-coordinates matrix. 7) Let B and C be bases for R², where Find the…

A:

Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

A:

Q: Let y = a. UTU= UUT 8 4 = II a. Let U be the 2 x 1 matrix whose only column is u₁. Compute UTU and…

A:

Q: 1. Two matrix vectors a and b are given as a = -0--0 and b Find (alb).

A:

Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

A:

Q: If A is an invertible matrix. Then det(AA-): 1D

A: IA is an invertible matrix To find det(AA-1)

Q: Suppose A is an n by n invertible matrix. Then A O True O False Suppose A and Bare n by n invertible…

A:

Q: Q 3.16 which of. the following oure ALWAYS true? O It A and 6 are レ matrices with det CAB) = 24 then…

A: Properties of the matrices

Q: -(¹-21) e matrix B x A? and B = (8) What is the entry on the row 2 and column

A: We have to find the 2nd row and 1st column of the matrix BA

Q: Which one of the following equations is true for nxn matrices A, B, and C? (Assume all matrices…

A: For the given matrices A, B, and C. We have to choose the correct option.

Q: 16 21 Let A = |-14 -19 Find two different diagonal matrices D and the corresponding matrix S such…

A: Given matrix is A=1621-14-19 We find the eigenvectors. For eigenvalues, A-λI=0⇒1621-14-19-λ…

Q: Prove why A-1=(ATA)-1AT is correct using the invertible matrix theorem

A:

Q: 1 -4-2) s) Let A := -2 3 2 4 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

A:

Q: 5. Is the matrix ㅇ 15 아가 Unitary? Explain. 블 ܐ ܥܙܐܡ ܝܐܐ ܙܐ3 춤을

A: A matrix is the arrangement of elements in a row and columns into a rectangular array. The order of…

Q: Consider the matrix distributive property. (c + d)A = CA + dA, where A is a matrix and c and d are…

A: Given Property is (c+d)A=cA+dA where A is matrix and c and d are scalarsGiven A=[aij]We know that…

Q: Let A be square matrix. I f A"=Onva %3D for Then A= Onen n > 2.

A:

Q: If A is a 2×2 matrix such that trace(A) = det(A) = 3, then %3D value of trace of (A-!) ?

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

A:

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

A:

Q: 1. Consider the matrix and and Monde Cole 2022 202) Mesh Colleg 202C) Mona that 1 1 0 101 0 1 1 Mo…

A:

Q: 6. For which positive integers n > 2 can V2 be constructed? Justify your answet

A:

Q: If A is a 2x2 matrix such that trace(A) = det(A) = 3, then what is the %3D value of trace of (A-!) ?…

A:

Q: 24. Let A [A₁, A2, A3] be a (3 × 3) matrix and set = 2 a) Show that B - 3 1 00 -1 ] 3 4 AB = [2A₁ +…

A: Here, the given A=A1, A2, A3 be a 3×3 matrix and set  B=2003-10134.

Q: matrix. 11) Let B=b1,b2 and C = 01, b2) and C= (c1, c2} be bases for, where 0₁ - [1] ₂2 - [-3].01 -…

A: