APPLIED LINEAR ALGEBRA TEST 1
QUESTIONS AND ANSWERS
Linear Equation - Answer-is in the variable X1,...,Xn is an equation in form
A1X1+A2X2+...+AnXn=b where Ai's and b are real or complex numbers
System of Linear Equations - Answer-A collection of one or more linear equations in the
same variables
Solution - Answer-(S1,...,Sn) is a list of numbers that satisfy each equation
Echelon Form - Answer-1) Each leading entry of a row is in a column to the right of the
leading entry of the row above it.
2)All entries in a column below a leading entry are zero
3) If there are rows of all zeros, they are at the bottom
Reduced Echelon Form - Answer-If the matrix satisfies the echelon form and includes
the conditions:
1) The leading entry in each nonzero row is 1
2) Each leading 1 is the only nonzero entry in its column
Pivot Position - Answer-in a matrix, it corresponds to a leading 1 in its reduced row
echelon form
Pivot Column - Answer-a column that contains a pivot
A Consistent Matrix - Answer-1) One solution to an augmented matrix: number of pivot
positions = number of variables
2) Infinitely many solutions: number of pivot positions is strictly less than number of
variables
An Inconsistent Matrix - Answer-No solution: system implies a false statement
Basic Variables - Answer-correspond to pivots
Free Variable - Answer-can be anything because it does not correspond to a pivot
Linear Combination - Answer-It is a vector W= C1V1+C2V2+...+CrVr, that combines the
vectors V1,V2,...,Vr and the scalars C1,C2,...,Cr.
Span R^n - Answer-The set of all linear combinations of v1,...,vn.
Matrix Multiplication - Answer-If A is an mXn matrix with columns A1,A2,...,An and if x is
a vector with R^n, then
QUESTIONS AND ANSWERS
Linear Equation - Answer-is in the variable X1,...,Xn is an equation in form
A1X1+A2X2+...+AnXn=b where Ai's and b are real or complex numbers
System of Linear Equations - Answer-A collection of one or more linear equations in the
same variables
Solution - Answer-(S1,...,Sn) is a list of numbers that satisfy each equation
Echelon Form - Answer-1) Each leading entry of a row is in a column to the right of the
leading entry of the row above it.
2)All entries in a column below a leading entry are zero
3) If there are rows of all zeros, they are at the bottom
Reduced Echelon Form - Answer-If the matrix satisfies the echelon form and includes
the conditions:
1) The leading entry in each nonzero row is 1
2) Each leading 1 is the only nonzero entry in its column
Pivot Position - Answer-in a matrix, it corresponds to a leading 1 in its reduced row
echelon form
Pivot Column - Answer-a column that contains a pivot
A Consistent Matrix - Answer-1) One solution to an augmented matrix: number of pivot
positions = number of variables
2) Infinitely many solutions: number of pivot positions is strictly less than number of
variables
An Inconsistent Matrix - Answer-No solution: system implies a false statement
Basic Variables - Answer-correspond to pivots
Free Variable - Answer-can be anything because it does not correspond to a pivot
Linear Combination - Answer-It is a vector W= C1V1+C2V2+...+CrVr, that combines the
vectors V1,V2,...,Vr and the scalars C1,C2,...,Cr.
Span R^n - Answer-The set of all linear combinations of v1,...,vn.
Matrix Multiplication - Answer-If A is an mXn matrix with columns A1,A2,...,An and if x is
a vector with R^n, then
