Chamberlain College
MATH_225 Statistical Reasoning for
the Health Science
2025/2026
Verified Questions and Answers
A+ Grades Guarantee
, Chamberlain College of Nursing
1. Augmented Matrix a coefficient matrix with an
extra column containing the
constant terms
2. Consistent system a system of equations or in-
equalities that has at least
one solution
3. Is the statement "Every elementary row operation is True, because replacement,
reversible" true or false? interchanging, and scaling
are all reversible.
4. Is the statement "A False, because a
5×6 5×6
matrix has six rows" true or false? matrix has five rows and six
columns.
5. Is the statement "The solution set of a linear system False, because the descrip-
involving variables tion applies to a single so-
x1...xn is a list of numbers (s1...sn) that makes each lution. The solution set con-
equation in the system a true statement when the sists of all possible solutions.
values s1....sn are subbed for x1...xn respectively"
true or false?
6. Is the statement "Two fundamental questions about True, because two funda-
a linear system involve existence and uniqueness" mental questions address
true or false? Explain. whether the solution exists
and whether there is only
one solution.
7. Echelon Form 1. All nonzero rows are above
any rows of all zeros.
2. Each leading entry of a
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row is in a column to the
right of the leading entry of
the row above it.
3. All entries in a column be-
low a leading entry are zeros.
8. Reduced Echelon Form Same as echelon form, ex-
cept 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
9. In some cases, a matrix may be row reduced to more The statement is false. Each
than one matrix in reduced echelon form, using dif- matrix is row equivalent to
ferent sequences of row operations. one and only one reduced
Is this statement true or false? echelon matrix.
10. The row reduction algorithm applies only to aug- The statement is false. The
mented matrices for a linear system. algorithm applies to any ma-
Is this statement true or false? trix, whether or not the ma-
trix is viewed as an aug-
mented matrix for a linear
system.
11. A basic variable in a linear system is a variable that The statement is true. It is
corresponds to a pivot column in the coefficient ma- the definition of a basic vari-
trix. able.
Is this statement true or false?
12. The statement is false. The
solution set of a linear sys-
MATH_225 Statistical Reasoning for
the Health Science
2025/2026
Verified Questions and Answers
A+ Grades Guarantee
, Chamberlain College of Nursing
1. Augmented Matrix a coefficient matrix with an
extra column containing the
constant terms
2. Consistent system a system of equations or in-
equalities that has at least
one solution
3. Is the statement "Every elementary row operation is True, because replacement,
reversible" true or false? interchanging, and scaling
are all reversible.
4. Is the statement "A False, because a
5×6 5×6
matrix has six rows" true or false? matrix has five rows and six
columns.
5. Is the statement "The solution set of a linear system False, because the descrip-
involving variables tion applies to a single so-
x1...xn is a list of numbers (s1...sn) that makes each lution. The solution set con-
equation in the system a true statement when the sists of all possible solutions.
values s1....sn are subbed for x1...xn respectively"
true or false?
6. Is the statement "Two fundamental questions about True, because two funda-
a linear system involve existence and uniqueness" mental questions address
true or false? Explain. whether the solution exists
and whether there is only
one solution.
7. Echelon Form 1. All nonzero rows are above
any rows of all zeros.
2. Each leading entry of a
, Chamberlain College of Nursing
row is in a column to the
right of the leading entry of
the row above it.
3. All entries in a column be-
low a leading entry are zeros.
8. Reduced Echelon Form Same as echelon form, ex-
cept 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
9. In some cases, a matrix may be row reduced to more The statement is false. Each
than one matrix in reduced echelon form, using dif- matrix is row equivalent to
ferent sequences of row operations. one and only one reduced
Is this statement true or false? echelon matrix.
10. The row reduction algorithm applies only to aug- The statement is false. The
mented matrices for a linear system. algorithm applies to any ma-
Is this statement true or false? trix, whether or not the ma-
trix is viewed as an aug-
mented matrix for a linear
system.
11. A basic variable in a linear system is a variable that The statement is true. It is
corresponds to a pivot column in the coefficient ma- the definition of a basic vari-
trix. able.
Is this statement true or false?
12. The statement is false. The
solution set of a linear sys-
