LINEAR ALGEBRA 7TH EDITION

LINEAR ALGEBRA 7TH EDITION
QUESTION: solution - ANSWER-A list (s1, s2, ..., sn) of numbers that makes each equation in the system a
true statement when the values s1, ..., sn are substituted for x1, ..., xn, respectively.




QUESTION: solution set - ANSWER-The set of all possible solutions of a linear system.




QUESTION: equivalent linear systems - ANSWER-Linear systems with the same solution set.




QUESTION: consistent linear system - ANSWER-A system with at least one solution.




QUESTION: inconsistent linear system - ANSWER-A system with no solutions.




QUESTION: matrix - ANSWER-A rectangular array of numbers.

Linear equation - ANSWER-An equation that can be written in the form a1x1 + a2x2 + ... + anxn = b,
where b and the coefficients a1, ..., an are real or complex numbers.




QUESTION: system of linear equations (linear system) - ANSWER-A collection of one or more linear
equations involving the same set of variables, say, x1, ... , xn.

, QUESTION: coefficient matrix - ANSWER-A matrix whose entries are the coefficients of a system of linear
equations.




QUESTION: augmented matrix - ANSWER-A matrix made up of a coefficient matrix for a linear system
and one or more columns to the right.




QUESTION: size - ANSWER-Two numbers, written in the form m x n, that specify the number of rows (m)
and columns (n) in the matrix.




QUESTION: m x n matrix - ANSWER-A matrix with m rows and n columns.




QUESTION: row equivalent - ANSWER-Two matrices for which there exists a finite sequence of row
operations that transforms one matrix into the other.




QUESTION: leading entry - ANSWER-The leftmost nonzero entry in a row of a matrix.




QUESTION: echelon matrix - ANSWER-A rectangular matrix that has three properties: (1) All nonzero
rows above any row of all zeros. (2) Each leading entry of a row is in a column to the right of the leading
entry of the row above it. (3) All entries in a column below a leading entry are zero.