LINEAR ALGEBRA: TERMINOLOGY EXAM QUESTIONS WITH CORRECT ANSWERS

LINEAR ALGEBRA: TERMINOLOGY
EXAM QUESTIONS WITH CORRECT
ANSWERS
linear equation - Answer-An equation that can be written in the form:

a1*x1* + a2*x2* + ... an*xn* = *b*

for some real (or complex) coefficient a1, a2... an and b.

linear system - Answer-A collection of one or more linear equations in the same
variables.

solution to a linear system - Answer-a list of values (s1, s2 ... sn) that simultaneously
satisfy all of the equations in system when substituted for x1x2...x3

solution set for a linear system - Answer-The set of all possible solutions for a linear
system.

consistent linear system - Answer-A linear system that has at least one solution

inconsistent linear system - Answer-A linear system that has no solutions

equivalent linear systems - Answer-linear systems that have the same solution set

row equivalent matrices - Answer-Matrices for which there is a sequence of elementary
row operations that will transform one matrix into another.

Two important questions we would like to answer for every linear system... - Answer--
Existence: Is the system consistent?
- Uniquiness: If the system is consistent, does it have a unique solution?

Characteristics of Echelon and reduced echelon form - Answer-

free variable - Answer-variables that do not belong to pivot columns, for which any value
may be chosen and which determines a different solution of the system.

basic variable - Answer-variables that do not belong to pivot columns, for which value(s)
are determined.

matrix size: m by n - Answer-row by column

leading entry - Answer-leftmost non-zero entry in a row