Does anyone else here use Maple?

[stayillogical]

for Math assignments in college. I hate it. It takes hours, only because there are a hundred different commands and you never know what to do. I have the simplest thing to input into the program right now, but have no idea how to get the answer. Sucks.

[jeffpike]

I use it quite a bit, I am a big fan.

[stayillogical]

Big fan, eh? Tell me... (or rather HELP)

Find all 2x2 matrices that satisfy a) A^2=I b) A^2=A

[jeffpike]

ok well it's been a while since I used maple for matrices (usually use matlab) but I'll give it a shot...

[jeffpike]

I am not sure if this works, but here goes. So assuming that I is the 2x2 identity matrix [1 0,0 1], create a matrix A=[m11 m12,m21 m22]. Then input the equation A^2=I. It will output a solution which is now simply one matrix equaling another. Now create 4 equations (knowing that the variables in 1,1 on the left must equal the value in 1,1 on the left, and so on). Then use solve({y1,y2,y3,y4}) and it should spit out a decent answer. A similar approach can be done for b)

[jeffpike]

I have done it, and it seems to give some reasonable answers. I have no clue if they are correct, but I tried. Good luck!

[stayillogical]

I am not sure if this works, but here goes. So assuming that I is the 2x2 identity matrix [1 0,0 1], create a matrix A=[m11 m12,m21 m22]. Then input the equation A^2=I. It will output a solution which is now simply one matrix equaling another. Now create 4 equations (knowing that the variables in 1,1 on the left must equal the value in 1,1 on the left, and so on). Then use solve({y1,y2,y3,y4}) and it should spit out a decent answer. A similar approach can be done for b)

This is the part I don't get. I had actually done up to that point but wasn't sure how to solve. What equations did you input? I think I had already done this but it didn't look right to me. Would it actually be as simple as setting the equations from the resulting A^2 matrix to the right values in I and solving? I mean, the question is asking for "all" matrices. Another matrix could also equal I by row reducing, or maybe I'm overthinking.

By the way, thank you very much kind stranger. I didn't think anyone with maple prowess would post here, especially so soon. This was only meant to vent. My assignment is actually do tomorrow and you're a big help.

[jeffpike]

my equations were something like y1:=m11^2+m12*m21-1, y2:=m11*m12+m12*m22, y3:=m21*m11+m22*m21, y4:=m12*m21+m22^2-1. Does this make any sense?

And it's really no problem at all. I really never post here, but I was bored today (my math programming assignment is way too hard) and saw this thread, and figured I could actually help a bit. I know what it's like to get stuck with this shit, it sucks.

[stayillogical]

I had practically the exact same thing when I originally did it. Damn. Thanks for reaffirming that. G'luck with your assignment.