If the Determinant is 0, what all is true? matrices fun

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SUMMARY

The discussion centers on the implications of a zero determinant in matrix equations, specifically the equation A = MX, where M is a 2x2 matrix. The determinant of M is calculated as m11m22 - m12m21. Participants agree that statements A and B are incorrect when the determinant is zero, as they pertain to unique solutions. The focus shifts to statements C, D, and E, which explore the existence of solutions when A equals zero, leading to the conclusion that multiple values of X may satisfy the equation under certain conditions.

PREREQUISITES
  • Understanding of matrix equations and notation
  • Knowledge of determinants and their significance in linear algebra
  • Familiarity with concepts of unique and multiple solutions in systems of equations
  • Basic skills in manipulating algebraic expressions
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  • Study the properties of determinants in linear algebra
  • Learn about the implications of singular matrices in systems of equations
  • Explore the concept of null space and its relation to solutions of matrix equations
  • Investigate the conditions under which a matrix has infinite solutions
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Students and professionals in mathematics, particularly those studying linear algebra, as well as educators seeking to clarify concepts related to determinants and matrix equations.

mr_coffee
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Hello everyone I'm stuck on this problem, how its wrong, i got parts a and c, but b i can't get. Hre is what it says:

Consider the following general matrix equation:
[a1 a2] =
|m11 m12| * [x1 x2]
|m21 m22|

which can also be written as A = MX
Determinant of M = m11m22 - m12m21

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

I said for sure A, and B are wrong because they are what happens if Det(M) is not equal to 0. so it has to be a combination of C,D, and E.

I tried like all combinations of C,D,and E, and nothing works!
 
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mr_coffee said:
I said for sure A, and B are wrong ...

You might go over your logic behind why you think that A is wrong.

Carl
 

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