MAT 101 GRADED EXAM 4 TOPIC 14 SOLVING
LINEAR SYSTEMS USING AUGMENTED
MATRICES 2026 COMPLETE QUESTIONS AND
ANSWERS GRADED A+ FULL SOLUTION
◉ True. Answer: The row reduction algorithm applies only to
augmented matrices for linear systems
◉ True. Answer: A basic variable in a linear system is a variable that
corresponds to a pivot column in the coefficient matrix
◉ True. Answer: Finding a parametric description of a solution set of
a linear system is the same as solving the system
◉ False. Answer: If one row in an echelon form of an augmented
matrix is {00050}, then the associated linear system is inconsistent
◉ False. Answer: The points in the plane corresponding to [-2, 5]
and [-5, 2] lie on a line through the origin
◉ True. Answer: An example of a linear combination of vectors v1
and v2 is 1/2v1
, ◉ True. Answer: The solution set of the linear system whose
augmented matrix [a1 a2 a3 b] is the same as a solution set of the
equation x1a1 + x2a2 + x3a3 = b
◉ False. Answer: The set span {u, v} is always visualized as a plain
through origin
◉ True. Answer: Any list of five real numbers is a vector in R5
◉ True. Answer: The vector u results when u-v is added to v
◉ False. Answer: the weights c1...cp in a linear combination
c1v1+...+cpvp cannot be zero
◉ True. Answer: when u and v are nonzero vectors, span {u, v}
contains the line through u and the origin
◉ True. Answer: Asking whether the linear system corresponding to
an augmented matrix [a1 a2 a3 b] has a solution amounts to asking
whether b is in span {a1, a2, a3}
◉ False. Answer: The equation Ax=b is referred to as a vector
equation
LINEAR SYSTEMS USING AUGMENTED
MATRICES 2026 COMPLETE QUESTIONS AND
ANSWERS GRADED A+ FULL SOLUTION
◉ True. Answer: The row reduction algorithm applies only to
augmented matrices for linear systems
◉ True. Answer: A basic variable in a linear system is a variable that
corresponds to a pivot column in the coefficient matrix
◉ True. Answer: Finding a parametric description of a solution set of
a linear system is the same as solving the system
◉ False. Answer: If one row in an echelon form of an augmented
matrix is {00050}, then the associated linear system is inconsistent
◉ False. Answer: The points in the plane corresponding to [-2, 5]
and [-5, 2] lie on a line through the origin
◉ True. Answer: An example of a linear combination of vectors v1
and v2 is 1/2v1
, ◉ True. Answer: The solution set of the linear system whose
augmented matrix [a1 a2 a3 b] is the same as a solution set of the
equation x1a1 + x2a2 + x3a3 = b
◉ False. Answer: The set span {u, v} is always visualized as a plain
through origin
◉ True. Answer: Any list of five real numbers is a vector in R5
◉ True. Answer: The vector u results when u-v is added to v
◉ False. Answer: the weights c1...cp in a linear combination
c1v1+...+cpvp cannot be zero
◉ True. Answer: when u and v are nonzero vectors, span {u, v}
contains the line through u and the origin
◉ True. Answer: Asking whether the linear system corresponding to
an augmented matrix [a1 a2 a3 b] has a solution amounts to asking
whether b is in span {a1, a2, a3}
◉ False. Answer: The equation Ax=b is referred to as a vector
equation
