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MATH 225 Exam 1 Questions And Answers
|Latest 2025 | Guaranteed Pass.
Augmented Matrix - Answer✔a coefficient matrix with an extra column containing the constant
terms
Consistent system - 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? - Answer✔True,
because replacement, interchanging, and scaling are all reversible.
Is the statement "A
5×6
matrix has six rows" true or false? - Answer✔False, because a
5×6
matrix has five rows and six columns.
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? - 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. - Answer✔True, because two fundamental questions
address whether the solution exists and whether there is only one solution.
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.
1
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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
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? - 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? - 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.
Is this statement true or false? - Answer✔The statement is true. It is the definition of a basic
variable.
Finding a parametric description of the solution set of a linear system is the same as solving the
system.
Is this statement true or false? - Answer✔The statement is false. The solution set of a linear
system can only be expressed using a parametric description if the system has at least one
solution.
f one row in an echelon form of an augmented matrix is [0 0 0 5 0] then the associated linear
system is inconsistent.
Is this statement true or false? - Answer✔The statement is false. The indicated row corresponds
to the equation
5x 4x4equals=0,
which does not by itself make the system inconsistent.
What must be true of a linear system for it to have a unique solution? Select all that apply. -
Answer✔The system is consistent, the system has no free variables
Use the augmented matrix to determine if the linear system is consistent. Is the linear system
represented by the augmented matrix consistent? - Answer✔Yes, because the rightmost
column of the augmented matrix is not a pivot column.
HW 2 #7 - Answer✔Rework
2
MATH 225 Exam 1 Questions And Answers
|Latest 2025 | Guaranteed Pass.
Augmented Matrix - Answer✔a coefficient matrix with an extra column containing the constant
terms
Consistent system - 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? - Answer✔True,
because replacement, interchanging, and scaling are all reversible.
Is the statement "A
5×6
matrix has six rows" true or false? - Answer✔False, because a
5×6
matrix has five rows and six columns.
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? - 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. - Answer✔True, because two fundamental questions
address whether the solution exists and whether there is only one solution.
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.
1
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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
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? - 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? - 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.
Is this statement true or false? - Answer✔The statement is true. It is the definition of a basic
variable.
Finding a parametric description of the solution set of a linear system is the same as solving the
system.
Is this statement true or false? - Answer✔The statement is false. The solution set of a linear
system can only be expressed using a parametric description if the system has at least one
solution.
f one row in an echelon form of an augmented matrix is [0 0 0 5 0] then the associated linear
system is inconsistent.
Is this statement true or false? - Answer✔The statement is false. The indicated row corresponds
to the equation
5x 4x4equals=0,
which does not by itself make the system inconsistent.
What must be true of a linear system for it to have a unique solution? Select all that apply. -
Answer✔The system is consistent, the system has no free variables
Use the augmented matrix to determine if the linear system is consistent. Is the linear system
represented by the augmented matrix consistent? - Answer✔Yes, because the rightmost
column of the augmented matrix is not a pivot column.
HW 2 #7 - Answer✔Rework
2
