Properties of Determinant=0 Okay, so I am dealing with a problem with determinant equal to 0. Admittedly, I do not know that much about determinant equal to 0 other than that it can cause no solution or infinitely many solutions.I think the first choice is true, but I do not know which of the others would be true or why. (My gut tells me that A&D would be true while the others are false but this is not based on any solid mathematical understanding.
$$
 \begin{bmatrix} a1 \\a2 \end{bmatrix}=\begin{bmatrix} m11 & m12 \\m21 & m22 \end{bmatrix}*\begin{bmatrix} x1 \\x2 \end{bmatrix}
$$
is abbreviated as A=MX
If det(M)=0, then which are true?
A. some values of A (such as A=0) will allow more than one X to satisfy the equation. 
B. given any X there is one and only one A which will satisfy the equation. 
C. there is no value of X which satisfies the equation when A=0. 
D. some values of A will have no values of X which will satisfy the equation.
E. given any A there is one and only one X which will satisfy the equation.

"Admittedly, I do not know that much about determinant equal to 0 other than that it can cause no solution or infinitely many solutions."
A. some values of A (such as A=0) will allow more than one X to satisfy the equation.
D. some values of A will have no values of X which will satisfy the equation.
E. given any A there is one and only one X which will satisfy the equation.
From the one thing you say you know.  Can you not see how that statement reflects directly on these 3.
B. given any X there is one and only one A which will satisfy the equation.
This does not hinge on your statement above.  But what if I told you that $M\mathbf x$ is a function of $\mathbf x$.  Would that give you any insight?
C. there is no value of X which satisfies the equation when A=0.
$M\mathbf 0 = \mathbf 0$ for any $M$
