MATH 225 Exam 1 Questions And Answers
Latest 2025
Augmented Matrix -
correct answer ✅a coefficient matrix with an extra column
containing the constant terms
Consistent system -
correct answer ✅a system of equations or inequalities that has at
least one solution
Is the statement "Every elementary row operation is reversible"
true or false? -
correct answer ✅True, because replacement, interchanging, and
scaling are all reversible.
Is the statement "A
5×6
matrix has six rows" true or false? -
correct answer ✅False, because a
5×6
matrix has five rows and six columns.
,MATH 225 Exam 1 Questions And Answers
Latest 2025
Is the statement "The solution set of a linear system involving
variables
x1...xn is a list of numbers (s1...sn) that makes each equation in the
system a true statement when the values s1....sn are subbed for
x1...xn respectively" true or false? -
correct answer ✅False, because the description applies to a single
solution. The solution set consists of all possible solutions.
Is the statement "Two fundamental questions about a linear system
involve existence and uniqueness" true or false? Explain. -
correct answer ✅True, because two fundamental questions
address whether the solution exists and whether there is only one
solution.
Echelon Form -
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.
, MATH 225 Exam 1 Questions And Answers
Latest 2025
Reduced Echelon Form -
correct 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
In some cases, a matrix may be row reduced to more than one
matrix in reduced echelon form, using different sequences of row
operations.
Is this statement true or false? -
correct answer ✅The statement is false. Each matrix is row
equivalent to one and only one reduced echelon matrix.
The row reduction algorithm applies only to augmented matrices
for a linear system.
Is this statement true or false? -
correct answer ✅The statement is false. The algorithm applies to
any matrix, whether or not the matrix is viewed as an augmented
matrix for a linear system.
A basic variable in a linear system is a variable that corresponds to a
pivot column in the coefficient matrix.
Latest 2025
Augmented Matrix -
correct answer ✅a coefficient matrix with an extra column
containing the constant terms
Consistent system -
correct answer ✅a system of equations or inequalities that has at
least one solution
Is the statement "Every elementary row operation is reversible"
true or false? -
correct answer ✅True, because replacement, interchanging, and
scaling are all reversible.
Is the statement "A
5×6
matrix has six rows" true or false? -
correct answer ✅False, because a
5×6
matrix has five rows and six columns.
,MATH 225 Exam 1 Questions And Answers
Latest 2025
Is the statement "The solution set of a linear system involving
variables
x1...xn is a list of numbers (s1...sn) that makes each equation in the
system a true statement when the values s1....sn are subbed for
x1...xn respectively" true or false? -
correct answer ✅False, because the description applies to a single
solution. The solution set consists of all possible solutions.
Is the statement "Two fundamental questions about a linear system
involve existence and uniqueness" true or false? Explain. -
correct answer ✅True, because two fundamental questions
address whether the solution exists and whether there is only one
solution.
Echelon Form -
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.
, MATH 225 Exam 1 Questions And Answers
Latest 2025
Reduced Echelon Form -
correct 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
In some cases, a matrix may be row reduced to more than one
matrix in reduced echelon form, using different sequences of row
operations.
Is this statement true or false? -
correct answer ✅The statement is false. Each matrix is row
equivalent to one and only one reduced echelon matrix.
The row reduction algorithm applies only to augmented matrices
for a linear system.
Is this statement true or false? -
correct answer ✅The statement is false. The algorithm applies to
any matrix, whether or not the matrix is viewed as an augmented
matrix for a linear system.
A basic variable in a linear system is a variable that corresponds to a
pivot column in the coefficient matrix.
