Linear Algebra I exam

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ElectricSheep

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May 11, 2000
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Linear Algebra isn't too bad, I just hope they don't make you invert a 4 by 4 matrix by HAND.

It does come in handy for things like numerically solving Laplace's Equations over all space for an irregularly mapped coordinate system.
 

Goat Fucker

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ES...you are a living calculator! its inhuman!

Ohh well, guess i should have showed up at school once in a while...on secound thought no, i was compleately right and justified in staying the hell away :D
 

ElectricSheep

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ES...you are a living calculator! its inhuman!

Ohh well, guess i should have showed up at school once in a while...on secound thought no, i was compleately right and justified in staying the hell away

Hehe.

This might frighten you, but I actually know how to take the square root and cube root of <em>any</em> given number (including decimals) by hand on a sheet of paper. Its kinda like long division, and helps in a pinch when you forget your calculator on an exam...
 

Catalyst

science begets death
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God damn you smart math people make me sick. I'm a programmer, could actually use the skills, and don't have them :(
 

agent

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Originally posted by ElectricSheep

This might frighten you, but I actually know how to take the square root and cube root of <em>any</em> given number (including decimals) by hand on a sheet of paper. Its kinda like long division, and helps in a pinch when you forget your calculator on an exam...

:rolleyes:

i can find the nth root of any number of arbitrary precision. the general algorithm is called Newton's Method in North American calculus textbooks and finding roots of real numbers is only one of its applications:

x_(i+1) = x_(i) - f(x_(i))/f'(x_(i)) (where x_(i)'s are approximations of the root of f)

and let

f(x) = x^n - a
then f'(x) = (n)x^(n-1)

to find the nth root of a.

[edit] check this out: http://mathworld.wolfram.com/NewtonsMethod.html
("A fractal is obtained by applying Newton's Method to finding a root of z^n - 1 = 0" ie.: nth complex root of 1) [/edit]
 
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Well, it's all over now. Going by my gut feeling I should have enough points.

@electric sheep: one of the things we had to do was inverting a 3*3 matrix... I half forgot how to do it. Grrr.

The rest was relatively ok. Eigenvalues, characteristic polynom, minimal polynom, determinants,...

Either way it's time to get drunk after I'm finished typing this :)
 

agent

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Originally posted by Puncher

@electric sheep: one of the things we had to do was inverting a 3*3 matrix... I half forgot how to do it. Grrr.

[ A | I ] ~ [ I | A^(-1)] if det(A) =/= 0 :p