338 ACTIVITY 2:
... We care because: Elementary matrices encode information on row operations. Each row operation can be carried out by multiplying our matrix from the left by the corresponding elementary matrix - a process that allows us to keep a record (by keeping track of the matrices) of the row operations. Rather ...
... We care because: Elementary matrices encode information on row operations. Each row operation can be carried out by multiplying our matrix from the left by the corresponding elementary matrix - a process that allows us to keep a record (by keeping track of the matrices) of the row operations. Rather ...
Module 4 : Solving Linear Algebraic Equations Section 3 : Direct
... Here, is a upper triangular matrix such that all elements below the main diagonal are zero and all the diagonal elements are non-zero, i.e. for all i. To solve the system , one can start from the last equation ...
... Here, is a upper triangular matrix such that all elements below the main diagonal are zero and all the diagonal elements are non-zero, i.e. for all i. To solve the system , one can start from the last equation ...
Solutions for Assignment 2
... Therefore we have the following cases: 1. if 2b−c−a 6= 0 then the RREF of the augmented matrix has an inconsistant row, therefore, the system has no solution. 2. If 2b − c − a = 0 then {(b − 2a + s, a − 2s, s) : s ∈ R} is the solution set for the system. So the system has infinitely many solutions ...
... Therefore we have the following cases: 1. if 2b−c−a 6= 0 then the RREF of the augmented matrix has an inconsistant row, therefore, the system has no solution. 2. If 2b − c − a = 0 then {(b − 2a + s, a − 2s, s) : s ∈ R} is the solution set for the system. So the system has infinitely many solutions ...
univariate case
... Theorem 12. Consider the set Pn of nonnegative univariate polynomials of degree less than or equal to n (n is even). Then, identifying a polynomial with its n + 1 coefficients (pn , . . . , p0 ), the set Pn is a proper cone (i.e., closed, convex, pointed, solid) in Rn+1 . An equivalent condition for t ...
... Theorem 12. Consider the set Pn of nonnegative univariate polynomials of degree less than or equal to n (n is even). Then, identifying a polynomial with its n + 1 coefficients (pn , . . . , p0 ), the set Pn is a proper cone (i.e., closed, convex, pointed, solid) in Rn+1 . An equivalent condition for t ...