LINEAR ALGEBRA PRACTICE EXAM
QUESTIONS AND ANSWERS
linear equation - Answer-a1x1+a2x2...+anxn=b
system of linear equations - Answer-collection of 1+ linear equations involving the same
variables
solution - Answer-list of numbers that makes each equation a true statement when the
values are substituted for the variables
solution set - Answer-set of all possible solutions of the linear system
equivalent linear systems - Answer-two linear systems are equivalent if they have the
same solution set
A system of linear equations has - Answer-1. no solution
2. exactly 1 solution
3. infinitely many solutions
coefficient matrix - Answer-matrix of just the coefficients of the variables
augmented matrix - Answer-matrix of the coefficients of the variables and the solutions
in the final column
size of matrix - Answer-m*n = m rows x n columns
3 operations to solving a linear system - Answer-1. replace one equation by the sum of
itself and a multiple of another equation
2. interchange two equations
3. multiply all terms in an equation by a nonzero constant
row equivalent - Answer-two matrices are row equivalent if there is a sequence of
elementary row operations that transforms one matrix into the other
Consistent system - Answer-has at least one solution
unique solution - Answer-if a solution exists, is it the only one?
inconsistent system - Answer-a system of linear equations with a row that resembles
the following:
( 0 0 0 15 )
leading entry - Answer-left most nonzero entry within a row
QUESTIONS AND ANSWERS
linear equation - Answer-a1x1+a2x2...+anxn=b
system of linear equations - Answer-collection of 1+ linear equations involving the same
variables
solution - Answer-list of numbers that makes each equation a true statement when the
values are substituted for the variables
solution set - Answer-set of all possible solutions of the linear system
equivalent linear systems - Answer-two linear systems are equivalent if they have the
same solution set
A system of linear equations has - Answer-1. no solution
2. exactly 1 solution
3. infinitely many solutions
coefficient matrix - Answer-matrix of just the coefficients of the variables
augmented matrix - Answer-matrix of the coefficients of the variables and the solutions
in the final column
size of matrix - Answer-m*n = m rows x n columns
3 operations to solving a linear system - Answer-1. replace one equation by the sum of
itself and a multiple of another equation
2. interchange two equations
3. multiply all terms in an equation by a nonzero constant
row equivalent - Answer-two matrices are row equivalent if there is a sequence of
elementary row operations that transforms one matrix into the other
Consistent system - Answer-has at least one solution
unique solution - Answer-if a solution exists, is it the only one?
inconsistent system - Answer-a system of linear equations with a row that resembles
the following:
( 0 0 0 15 )
leading entry - Answer-left most nonzero entry within a row
