Math 208 Exam Questions with Verified Correct
Answers
Consider the accompanying matrix as the augmented matrix of a linear system. State in
words the next two elementary row operations that should be performed in the process of
solving the system.
1 −6 4 0 −2
0 2 −6 0 5
0 0 1 4 −3
0 0 4 13 −3
What should be the first elementary row operation performed? Select the correct choice
below and, if necessary, fill in the answer box to complete your choice.
Replace row 4 by its sum with −4
times row 3.
What should be the second elementary row operation performed? Select the correct choice
below and, if necessary, fill in the answer box to complete your choice.
Scale row 4 by
−1/3.
The augmented matrix of a linear system has been reduced by row operations to the form
shown. Continue the appropriate row operations and describe the solution set of the
original system.
000−3
01−14
,0013
172−3
Select the correct choice below and, if necessary, fill in the answer boxes to complete your
choice.
The solution set is empty.
The augmented matrix of a linear system has been reduced by row operations to the form
shown. Continue the appropriate row operations and describe the solution set of the
original system.
1−290
0170
0060
Select the correct choice below and, if necessary, fill in the answer boxes to complete your
choice.
The solution set contains one solution,
(0,0,0).
The augmented matrix of a linear system has been reduced by row operations to the form
shown. Continue the appropriate row operations and describe the solution set of the
original system.
1−300−4
01−10−6
,001−22
00014
The solution set contains one solution:
(8,4,10,4).
Solve the system.
x1 −6x3 =22
4x1+2x2−9x3=49
x2+5x3=−12
The unique solution of the system is
(4, 3, −3).
Do the three planes
x1+4x2+x3=4,x2−x3=1,
and 3x1+15x2=8 have at least one common point of intersection? Explain.
The three planes do not have a common point of intersection.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
1h4
-5 10 -24
The matrix is the augmented matrix of a consistent linear system if h≠−2.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
, 1 2 -5
4 h -20
The matrix is the augmented matrix of a consistent linear system for every value of h.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
8 14 h
-4 -7 3
The matrix is the augmented matrix of a consistent linear system if
h=−6.
Determine whether the statement below is true or false. Justify the answer.
Every elementary row operation is reversible.
The statement is true. Replacement, interchanging, and scaling are all reversible.
Determine whether the statement below is true or false. Justify the answer.
Elementary row operations on an augmented matrix never change the solution set of the
associated linear system.
The statement is true. Each elementary row operation replaces a system with an equivalent
system.
Determine whether the statement below is true or false. Justify the answer.
A 5×6 matrix has six rows.
The statement is false. A 5×6 matrix has five rows and six columns.
Answers
Consider the accompanying matrix as the augmented matrix of a linear system. State in
words the next two elementary row operations that should be performed in the process of
solving the system.
1 −6 4 0 −2
0 2 −6 0 5
0 0 1 4 −3
0 0 4 13 −3
What should be the first elementary row operation performed? Select the correct choice
below and, if necessary, fill in the answer box to complete your choice.
Replace row 4 by its sum with −4
times row 3.
What should be the second elementary row operation performed? Select the correct choice
below and, if necessary, fill in the answer box to complete your choice.
Scale row 4 by
−1/3.
The augmented matrix of a linear system has been reduced by row operations to the form
shown. Continue the appropriate row operations and describe the solution set of the
original system.
000−3
01−14
,0013
172−3
Select the correct choice below and, if necessary, fill in the answer boxes to complete your
choice.
The solution set is empty.
The augmented matrix of a linear system has been reduced by row operations to the form
shown. Continue the appropriate row operations and describe the solution set of the
original system.
1−290
0170
0060
Select the correct choice below and, if necessary, fill in the answer boxes to complete your
choice.
The solution set contains one solution,
(0,0,0).
The augmented matrix of a linear system has been reduced by row operations to the form
shown. Continue the appropriate row operations and describe the solution set of the
original system.
1−300−4
01−10−6
,001−22
00014
The solution set contains one solution:
(8,4,10,4).
Solve the system.
x1 −6x3 =22
4x1+2x2−9x3=49
x2+5x3=−12
The unique solution of the system is
(4, 3, −3).
Do the three planes
x1+4x2+x3=4,x2−x3=1,
and 3x1+15x2=8 have at least one common point of intersection? Explain.
The three planes do not have a common point of intersection.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
1h4
-5 10 -24
The matrix is the augmented matrix of a consistent linear system if h≠−2.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
, 1 2 -5
4 h -20
The matrix is the augmented matrix of a consistent linear system for every value of h.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent
linear system.
8 14 h
-4 -7 3
The matrix is the augmented matrix of a consistent linear system if
h=−6.
Determine whether the statement below is true or false. Justify the answer.
Every elementary row operation is reversible.
The statement is true. Replacement, interchanging, and scaling are all reversible.
Determine whether the statement below is true or false. Justify the answer.
Elementary row operations on an augmented matrix never change the solution set of the
associated linear system.
The statement is true. Each elementary row operation replaces a system with an equivalent
system.
Determine whether the statement below is true or false. Justify the answer.
A 5×6 matrix has six rows.
The statement is false. A 5×6 matrix has five rows and six columns.
