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Discrete Mathematics
Discrete Mathematics Exam
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Q.1
The linear system Cx = d is known as _________ if d! = 0.
a) homogeneous
b) heterogeneous
c) nonhomogeneous
d) augmented system
Q.2
Every linear equation determines a _______ in n-dimensional space for n variables.
a) shipshape
b) hyperplane
c) cone
d) pyramid
Q.3
Determine all possibilities for the number of solutions of the system of 7 equations in 5 unknowns and it has x1 =x2 = −and x3 = 4 as a solution.
a) unique or infinitely many
b) unique
c) finitely many
d) zero
Q.4
Determine all possibilities for the solution set of the homogeneous system that has y1 =y2 = −y3 = 0 as a solution.
a) zero
b) infinitely many
c) finitely many
d) only one
Q.5
Determine all possibilities for the solution set of the homogeneous system of 5 equations in 3 unknowns and the rank of the system is 3.
a) more than two
b) only one
c) zero
d) infinite
Q.6
Determine all possibilities for the solution set of a homogeneous system that has y1 =y2 = −y3 = 2 as a solution.
a) one
b) finitely many
c) infinitely many
d) either one or infinitely many
Q.7
Determine all possibilities for the solution set of the system of 2 equations in 3 unknowns that has x1 =x2 = −x3 = 0 as a solution.
a) one or finitely many
b) infinite
c) finite
d) zero
Q.8
Determine all possibilities for the solution set of a homogeneous system of 4 equations in 4 unknowns.
a) only one
b) finitely many or zero
c) zero
d) one or infinitely many
Q.9
Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.
a) only one
b) zero
c) one or infinitely many
d) finitely many
Q.10
Determine all possibilities for the solution set of a homogeneous system of 5 equations in 4 unknowns and the rank of the system is 3.
a) finite
b) zero or finitely many
c) only one
d) infinite
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