LINEAR ALGEBRA - EXAM 1 - THINGS
TO KNOW- QUESTIONS AND ANSWERS
Linear System - Answer-Two or more linear equations that share the same variables
mxn linear system - Answer-A linear system with m equations and n unknowns
Solving a linear system - Answer-Find the values of all unknowns such that each
equation is satisfied
Consistent System - Answer-A system of equations that has at least one solution
Inconsistent System - Answer-A system of equations that has no solution.
Matrix - Answer-A rectangular array of numbers
Elementary Row Operations - Answer-1. (Replacement) Replace one row by the sum of
itself and a multiple of another row.
2. (Interchange) Interchange two rows
3. (Scaling) Multiply all entries in a row by a nonzero constant
back substitution - Answer-The process of solving a linear system of equations that has
been transformed into row-echelon form or reduced row-echelon form. The last
equation is solved first, then the next-to-last, etc.
Strict Triangle Form - Answer-A square matrix where either side of the diagonal is full of
zeros.
Row Echelon Form - Answer-1. The first nonzero entry in each row is 1
2. The number of leading zero entries in the kth row < in the (k-1)th row
3. Any zero rows are at the bottom of the matrix
Gaussian Elimination - Answer-Sequence of elementary row operations on a matrix of
coefficients and answers to transform the matrix into row echelon form
Reduced Row Echelon Form - Answer-1. the matrix is in row echelon form
2. the first nonzero entry in each row is the only nonzero entry in its column
Gauss-Jordan Elimination - Answer-The process of using elementary row operations to
transform a matrix into reduced row echelon form
Equivalent Matrices - Answer-Two matrices are equivalent if their dimensions are the
same and the entries in corresponding positions are equal.
TO KNOW- QUESTIONS AND ANSWERS
Linear System - Answer-Two or more linear equations that share the same variables
mxn linear system - Answer-A linear system with m equations and n unknowns
Solving a linear system - Answer-Find the values of all unknowns such that each
equation is satisfied
Consistent System - Answer-A system of equations that has at least one solution
Inconsistent System - Answer-A system of equations that has no solution.
Matrix - Answer-A rectangular array of numbers
Elementary Row Operations - Answer-1. (Replacement) Replace one row by the sum of
itself and a multiple of another row.
2. (Interchange) Interchange two rows
3. (Scaling) Multiply all entries in a row by a nonzero constant
back substitution - Answer-The process of solving a linear system of equations that has
been transformed into row-echelon form or reduced row-echelon form. The last
equation is solved first, then the next-to-last, etc.
Strict Triangle Form - Answer-A square matrix where either side of the diagonal is full of
zeros.
Row Echelon Form - Answer-1. The first nonzero entry in each row is 1
2. The number of leading zero entries in the kth row < in the (k-1)th row
3. Any zero rows are at the bottom of the matrix
Gaussian Elimination - Answer-Sequence of elementary row operations on a matrix of
coefficients and answers to transform the matrix into row echelon form
Reduced Row Echelon Form - Answer-1. the matrix is in row echelon form
2. the first nonzero entry in each row is the only nonzero entry in its column
Gauss-Jordan Elimination - Answer-The process of using elementary row operations to
transform a matrix into reduced row echelon form
Equivalent Matrices - Answer-Two matrices are equivalent if their dimensions are the
same and the entries in corresponding positions are equal.
