DescriptionSolve linear systems of equations and compute inverses, while also showing your work.
This is an upgrade of the famous http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref
It also contains some other extra programs, that I thought could be uploaded too as a bonus. So, enjoy.
This update uses artificial modulus and divide functions so that the overflow error doesn't happen, it now supports arbitrarily large dataset operations, as well as some other new features such as computing the determinant.InstructionsUse the circle pad, and other buttons including L and R to navigate.
Use the touch screen for everything else.
Say you want to solve:
1x + 3y - 2z = 5
3x + 5y + 6z = 7
2x + 4y + 3z = 8
You can use substitution and elimination like highschool teachers teach... or more elegantly input them into a matrix:
1 3 -2 5
3 5 6 7
2 4 3 8
And convert it to Reduced Row Echelon Form (RREF):
1 0 0 -15
0 1 0 8
0 0 1 2
And now you can see that:
x = -15
y = 8
z = 2
Let's test that these values are correct by plugging them in:
1(-15) + 3(8) - 2(2) = 5 True
3(-15) + 5(8) + 6(2) = 7 True
2(-15) + 4(8) + 3(2) = 8 True
Similarly, we can compute the inverse by concatenating an identity matrix to the end:
1 3 -2 1 0 0
3 5 6 0 1 0
2 4 3 0 0 1
Convert to RREF:
1 0 0 9/4 17/4 -7
0 1 0 -3/4 -7/4 3
0 0 1 -1/2 -1/2 1
And now the inverse is on the right side. Multiplying the original array by it's inverse will return an identity matrix, i.e.
1 0 0
0 1 0
0 0 1
Multiplying the inverse by the three output values: 5, 7, 8, will return the answers: -15, 8, 2.
If you need any homework help, comment below, and I may or may not help you :)
2 Comment(s)spaceturtlesVideo GamesI like to play video games!HobbiesAvatar BlockI didn't change my avatar for 30 days.WebsiteIntermediate ProgrammerI can make programs, but I still have trouble here and there. Programming StrengthNice, something I can use for my math tests!Super_DefaultioVideo GamesI like to play video games!HobbiesDay PersonI like the warm sunshine and wake up early!Express YourselfZelda Is Awesome!I love The Legend Of Zelda!Express YourselfWow, this is pretty neat! It's like, some sort of advanced calculator for Linear Algebra or something!
