# f11hw3 - Homework 3 Chapter 2 Sections 4 5*UPDATE Due...

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Homework 3: Chapter 2, Sections 4, 5 [**UPDATE**] Due Monday, Feb 7

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2 Section 2.4: Row Reduction (Monday) 2.5: Gaussian Elimination (moved to Friday) 2.6 Inverses (moved to next week)
Linear Systems If A is an m × n matrix with entries a i,j , vectorx is the n -column vector with entries x 1 ,...x n , and vector b is the m -column vector with entries b 1 ,...b m , the matrix equation Avectorx = vector b gives m equations, each of the form ( i th row of A ) · vectorx = b i , which is called a linear system of m equations in n variables. In the equation Avectorx = vector b, the matrix A is called the coefficient matrix of the system, and vectorx and vector b are called the vector of unknowns and the right-hand side vector, respectively.

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4 Our preliminary qualitative description of the solutions of these systems (in 2-space and 3-space) suggests three cases: (1) just one unique solution; (2) no solutions; or (3) infinitely many solns. We say that the system of equations is consistent if there is at least one solution; and inconsistent if there are no solutions. Two systems with the same solutions are called equivalent. Our objective is to replace a given system by the simplest possible equivalent system. For the calculations - we don’t use the equations, but instead one more matrix A # = ( A | vector b ) , which is called the augmented matrix of the system.
Problem 3.

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