Computational Linear Algebra Exam 1
Questions And Answers Latest 2025
Row Echelon Form (REF) - - -
correct 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 Row Echelon Form (RREF) - - -
correct answer ✅(In REF)
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.
4. All leading entries are 1
5. In a column with a leading 1, all other elements are 0.
Uniqueness of the Reduced Echelon Form - - -
correct answer ✅Each matrix is row equivalent to one and only
one reduced echelon matrix.
(Is it consistent? If so, is there only one solution(free variables or
not)?)
, Computational Linear Algebra Exam 1
Questions And Answers Latest 2025
pivot column - - -
correct answer ✅A column that contains a pivot position
pivot positon - - -
correct answer ✅In A is a location that corresponds to a pivot
Rank(A) (rank of A) - - -
correct answer ✅the number of pivot positions in a matrix A in ref
and rref (should be equal for ref and rref)
(True or False?): If the system is inconsistent, the solution set is
empty, even when the system has free variables. - - -
correct answer ✅True
What is the name given to the variables that correspond with the
pivot columns? - - -
correct answer ✅pivot variables or (basic variables, if you are a
weirdo)
Questions And Answers Latest 2025
Row Echelon Form (REF) - - -
correct 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 Row Echelon Form (RREF) - - -
correct answer ✅(In REF)
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.
4. All leading entries are 1
5. In a column with a leading 1, all other elements are 0.
Uniqueness of the Reduced Echelon Form - - -
correct answer ✅Each matrix is row equivalent to one and only
one reduced echelon matrix.
(Is it consistent? If so, is there only one solution(free variables or
not)?)
, Computational Linear Algebra Exam 1
Questions And Answers Latest 2025
pivot column - - -
correct answer ✅A column that contains a pivot position
pivot positon - - -
correct answer ✅In A is a location that corresponds to a pivot
Rank(A) (rank of A) - - -
correct answer ✅the number of pivot positions in a matrix A in ref
and rref (should be equal for ref and rref)
(True or False?): If the system is inconsistent, the solution set is
empty, even when the system has free variables. - - -
correct answer ✅True
What is the name given to the variables that correspond with the
pivot columns? - - -
correct answer ✅pivot variables or (basic variables, if you are a
weirdo)
