1-2 | Quiz 1

Question 1

Given the matrix

M =
1 0 3
4 -1 4

which of the following vectors is in the null space of M?

A = [-2 -3]^T
B = [3 8 -1]^T
C = [3 8 -1]
D = [0 2 0]^T

Answer 1

B = [3 8 -1]^T

Question 2

Given the matrix

M =
1 0 3
4 -1 4

which of the following vectors can multiply M from the left?

A = [4 8 ]^T
B = [3 8 -1]
C = [1 0 4]^T
D = [5 8]

Answer 2

D = [5 8]

Question 3

Given the matrix

M =
1 0 3
4 -1 4

for which of the following matrices, N, the product MN exists:

1 0 3 ^T
3 1 -2

2
1

1 4 2
3 0 1

1 0 2

Answer 3

1 0 3 ^T
3 1 -2

Question 5

Given the matrix

M =
1 0 3
4 -1 4

What is the rank of M?

Answer 5

2

Question 6

True or false:

The decision variables in a canonical form of a linear programming problem can only take non-negative values.

Answer 6

True

Question 7

True or False?

(B + A)^T = A^T + B^T

Answer 7

True

Question 8

True or false:

The system of linear equations:
[ 1 2; 2 3 ] [ x ; y ] = [ 2 ; 3 ]
is incosistent

Answer 8

false

Question 9

Given a linear program, a boundary point that is not a vertex of its feasible region can optimize the objective.

Answer 9

false

Question 10

True or false

There exists a linear program with multiple optima for the objective function.

Answer 10

false

Question 12

True or false?

The Simplex method can be used when all constraints are linear equalities.

Answer 12

True