LINEAR ALGEBRA TEST REVIEW
QUESTIONS WITH CORRECT ANSWERS
Linear Equation - Answer-can be written in the form a1x1+a2x2+...+anxn=b
collection of one or more linear equations involving the same variables - Answer-system
of linear equations
consistent - Answer-A system of equations that has at least one solution
inconsistent - Answer-no solution
Coefficent matrix - Answer-just coefficients of the equation
Augmented matrix - Answer-has coefficients and the solutions
row equivalent matrices - Answer-Two matrices where one matrix can be transformed
into the other matrix by a sequence of elementary row operations.
Echelon Form - Answer-1. All nonzero rows are above any rows 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 zeros.
Reduced Echelon Form - Answer-Same as echelon form, except all leading entries are
1; each leading 1 is the only non-zero entry in its row; there is only one unique reduced
echelon form for every matrix
pivot position - Answer-in a matrix A is a location in A that corresponds to a leading 1 in
RREF
pivot column - Answer-A column that contains a pivot position
basic variable - Answer-a variable in a linear system that corresponds to a pivot column
in the coefficient matrix
free variable - Answer-any variable in a linear system that is not a basic variable
vector - Answer-matrix with one column
linear combination - Answer-A sum of scalar multiples of vectors. The scalars are called
the weights.
subset - Answer-a set that is part of a larger set
QUESTIONS WITH CORRECT ANSWERS
Linear Equation - Answer-can be written in the form a1x1+a2x2+...+anxn=b
collection of one or more linear equations involving the same variables - Answer-system
of linear equations
consistent - Answer-A system of equations that has at least one solution
inconsistent - Answer-no solution
Coefficent matrix - Answer-just coefficients of the equation
Augmented matrix - Answer-has coefficients and the solutions
row equivalent matrices - Answer-Two matrices where one matrix can be transformed
into the other matrix by a sequence of elementary row operations.
Echelon Form - Answer-1. All nonzero rows are above any rows 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 zeros.
Reduced Echelon Form - Answer-Same as echelon form, except all leading entries are
1; each leading 1 is the only non-zero entry in its row; there is only one unique reduced
echelon form for every matrix
pivot position - Answer-in a matrix A is a location in A that corresponds to a leading 1 in
RREF
pivot column - Answer-A column that contains a pivot position
basic variable - Answer-a variable in a linear system that corresponds to a pivot column
in the coefficient matrix
free variable - Answer-any variable in a linear system that is not a basic variable
vector - Answer-matrix with one column
linear combination - Answer-A sum of scalar multiples of vectors. The scalars are called
the weights.
subset - Answer-a set that is part of a larger set
