Finding Solutions for a Matrix with Variables: Row Reduction Required?

[rhuelu]

here's a tough one...

find the values of x for which the matric has no, one, and inf many solutions

A= (1 -2 3 1; 2 x 6 6; -1 -3 x-3 0)

 

[NoMoreExams]

What do all those mean to you? I.e. what properties does a matrix that has no solutions have? What about one solution? What about infinitely many? You can think of these geometrically, what does it mean (geometricall) to have no solutions? one? infinitely many?

 

[HallsofIvy]

What have you done? If you want, as your title implies the the "row reduced echelon form", then go ahead and do the row reduction! The fact that "x" is a variable only means you have to use a little algebra rather than just arithmetic. That probably will involve fractions that have some function of x as the denominator. Obviously, values of x that make the denominator 0 will give difficulties.

I do feel compelled to point out that a matrix doesn't have a "solution". If you are asking for which values of x does the matrix equation has one, no, or infinitely many solutions, you will have to have an equation!