Consider the following general matrix equation:

⎡⎣⎢⎢[ a1 ⎤⎦⎥⎥]
a2 ==
⎡⎣⎢⎢[ m11 m12 ⎤⎦⎥⎥]
m21 m22
⎡⎣⎢⎢[ x1 ⎤⎦⎥⎥]
x2

which can also be abbreviated as:

A=MX

By definition, the determinant of M is given by

det(M)=m11m22−m12m21

The following questions are about the relationship between the determinant of M and the ability to solve the equation above for A in terms of X or for X in terms of A.
Check the boxes which make the statement correct:
If the det(M)≠0 then

A. some values of X will have more than one value of A which satisfy the equation.
B. given any X there is one and only one A which will satisfy the equation.
C. some values of A (such as A=0 ) will allow more than one X to satisfy the equation.
D. given any AA there is one and only one X which will satisfy the equation.
E. some values of A will have no values of X which will satisfy the equation.
F. some values of X will have no values of A which satisfy the equation.

Check the boxes which make the statement correct:
If the det(M)=0 then

A. given any A there is one and only one X which will satisfy the equation.
B. some values of A will have no values of X which will satisfy the equation.
C. there is no value of X which satisfies the equation when A=0 .
D. some values of A (such as A=0 ) will allow more than one X to satisfy the equation.
E. given any X there is one and only one A which will satisfy the equation.

Check the conditions that guarantee that det(M)=0 :

A. There is some value of A for which no value of X satisfies the equation.
B. Given any A the is one and only one X which will satisfy the equation.
C. When A=0 there is more than one X which satisfies the equation.
D. Given any X there is one and only one A which will satisfy the equation