Please teach how to solve not just solveA matrix is idempotent if, when multiplied by itself it yields itself. That is, A is idempotent if AA = Aa) When is the matrix (b) idempotent?b) Consider a diagonal matrix of the following form:if its diagonal elements are either 1 or 0.a11I0⠀ Prove that such a matrix will be idempotentannConsider two matrices A, B. Assuming these are well defined for the following operations, demonstrate whether thefollowing operation results in a symmetric and idempotent matrix:(AB) ((AB)'(AB))¹(AB)'

Given That: Idempotent Matrix A=abcd Diagonal Matrix M=a11...0⋮⋱⋮0…ann To Find : a) Condition When…

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following two statements are from the Invertible Matrix Theorem about an n x n matrix A. Statement 1: "The equation Aï = 0 has only the trivial solution." Statement 2: "The columns of A form a linearly independent set." EXPLAIN how Statement 1 implies Statement 2. EXPLAIN how Statement 2 implies Statement 1. (a) (b)
For a square matrix A, AA™ = A™A. A) True B False
2. (i) A square matrix A is called idempotent if A? = A. Find all %3D 2 x 2 matrices A over the real numbers which are idempotent and aij # 0 for i, j = 1, 2. (ii) Let A, B be n x n idempotent matrices. Show that A+B are idempotent if and only if AB = BA = 0n.
In which of the scripts that follow matrix R is an orthonormal (or orthogonal) matrix. Remember, an orthogonal matrix is one whose transpose is its inverse. This means that if we multiply a matrix by its inverse the result is the identity matrix. Select one: a. A=rand(3,3);R = A + inv(A) b. A=rand(3,3);S=A-A'R = (eye(3)-S)*(eye(3)+S); c. A=rand(3,3);R = A + inv(A') d. A=rand(3,3);R = A - inv(A) e. A=rand(3,3);S=A-A'R = inv(eye(3)-S)*(eye(3)+S);
If A = (aij) is a matrix of order 5 ⨯ 4 and aij = -4 for all i and j, write down A. (Enter NONE in any unused answer blanks.) A =
please solve this question asap
Abstract Algebra
a) Matrix A has elements a1 = 1+I, a12 = 1-i, az1 = 1-1, az2 = 1+i Show that if Matrix A is divided by 2 then it will become Unitary Matrix. %3D
Which of the following matrices is positive definite?
Provide complete arguments/proofs for the following. a) A is invertible iff there exists a matrix B so that AB = BA = I. It is simple to show that: (i) If A is invertible and AB = I, then BA = I as well and B is the unique such matrix. (ii) If A is invertible and BA = I, then AB = I as well and B is the unique such matrix. This shows that if A is invertible, then there is a unique matrix B such that AB = I or BA = I. Call this unique matrix A-1. The goal here is to show that the assumption “A is invertible” is not needed in (i) or (ii). Prove: Let A and B be square matrices with AB = I. Show that A is invertible and hence B = A-1. b) Prove: NS(A) = NS(AT A) for any matrix A. c) Prove: If A and B are m x n matrices such that Ax = Bx for all x∈ Rn, then A = B.

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