2 replies to this topic

[jwxie518]

I am doing this in matlab. But what I am more into is the concepts behind it.
I don't understand the aspects of matrices infinite.

Let say I have 3 x 3 matrix

A = [ (A1) 2 3; 2 3 4; 4 4 5 ]
b = [ (b1); 2; 3]
A1 = alpha
b1 = beta
these are variables and the only things we can input.

I want to find all three conditions:
case 1 det =/ 0 - > unique solution
case 2 det = 0, no solution
case 3 infinite solution

I am actually writing a program for these 3 cases. I am only allow to change A1 and b2 (they are variables). I know how to program them. But what I don't understand is the concept of matrices in terms of the 3 cases.

Can someone explains, how does one gets case 3?
for case 1 and case 2, we can basically use det(A) zero or not equal to zero to determine the case (answer)
but for the 3rd case, how do you define a rule? what is the concept behind it?

I have tried a few cases for case 3 and did work out with NaN, -Inf, Inf but then again, only a and b are allowed to change. there must be a general definition to 3rd case.

[WingedPanther]

I wouldn't bother with MatLab for this.

Work out det(A) as a function of alpha. All values where det(A) is not 0 are unique solutions.

For the one value of alpha where det(A) = 0, I would use row reduction on the system to find the values of beta that produce an inconsistent (no solutions) or consistent (infinite solutions) system.

[jwxie518]

Hi Panther,

Thanks for the help. I probably had thought too much which led to the wrong direction. Now after a few days of reading and learning, I think I am on the right track.
John Wong's Blog working on matrices 3x3 in Matlab (2) - Just another Lively' Star....