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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.

John Hughes
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user345
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1 Answers1

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"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 $M$

Doug M
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