Anyone good with Linear Algebra?

[EtherealMystic]

I'm doing my homework and have these 3 problems left, but I have no idea how to approach them...

Any help would be appreciated!

 

[G-Lexington]

I got my degree in linear algebra/differential equations.
In 1992.
And haven't looked at it since.
Sorry.

Lex

 

[EtherealMystic]

Full of sads.

 

[EtherealMystic]

I have no musical talent, sadly.

 

[Corny]

you should have done similar problems before. at least for 2 and 3. 2 can also be solved with any mathematica like program.

 

[EtherealMystic]

I probably have but the different ways it is asked just throws me off.

This class I have to use MapleSoft and as I've never used it before I wouldn't really know where to begin. This summer class is quiet fast paced so he doesn't really go over every type of questions he could ask...

Hopefully I will figure it out sooner or later.

 

[gsdx]

Be patient. There are a few math wizard here. They'll show up and help you, I'm sure.

 

[Butter My Biscuits]

sorry I just had too

 

[EtherealMystic]

I have managed to figure out #3. #1 I did it, but I'm not sure if it is right or not. Only #2 left!

 

[EtherealMystic]

View attachment 825067View attachment 825068

sorry I just had too

That was a good movie.

 

[oakpope]

2 is really easy, it's just a system of 3 unknown in three equations :

you need to search alpha (a), beta (b) and gamma (c) so that :

a+b+c = 0 (1)
2a +4c = 0 (2)
3a + 2b +4c = 0 (3)

(2) gives you a = -2c
you replace a in (1) and (3) by -2c you got
b - c = 0 (1')
2b - 2c = 0 (3')

so, any real numbers can be b and c and a is -2c

 

[oakpope]

for #1 and #3 you need to search for definitions. You apply calculus rules to the matrix and you will find the solutions. It's really only definition applications here.

for #3, a) and b) are definition application and calculus. Once you have established a) and b) you get c) trivially
as c) = a) + b) :
1/2(A + At) + 1/2(A - At) = A (duh !)
d) is just an example of what you just have done, all you need to do is calculate A (duh ! it's A !) and At (so the transform form of A). Again just application of definition.

good luck

 

[EtherealMystic]

Thanks oakpope. I got the same answers as you for #2 and #3. I'm just having a hard time explaining #1, I think I'm making it harder than it should be.

 

[ashonfire]

for #1 and #3 you need to search for definitions. You apply calculus rules to the matrix and you will find the solutions. It's really only definition applications here.

for #3, a) and b) are definition application and calculus. Once you have established a) and b) you get c) trivially
as c) = a) + b) :
1/2(A + At) + 1/2(A - At) = A (duh !)
d) is just an example of what you just have done, all you need to do is calculate A (duh ! it's A !) and At (so the transform form of A). Again just application of definition.

good luck

That's some sexy Algebra-ing!

 

[oakpope]

Thanks oakpope. I got the same answers as you for #2 and #3. I'm just having a hard time explaining #1, I think I'm making it harder than it should be.

you're welcome ! for #1 I am not familiar with the English expression, so it's more difficult for me to help you (I'm French, sorry )

 

[oakpope]

for #1 this code (from wiki) will give you the result, but you should explain yourself the calculus, so understand the program and search in your books the validation for it :

function ToRowEchelonForm(Matrix M) is
nr := number of rows in M
nc := number of columns in M

for 0 ≤ r < nr do
allZeros := true
for 0 ≤ c < nc do
if M[r, c] != 0 then
allZeros := false
exit for
end if
end for
if allZeros = true then
In M, swap row r with row nr - 1
nr := nr - 1
end if
end for

p := 0
while p < nr and p < nc do
label nextPivot:
r := 1
while M[p, p] = 0 do
if (p + r) <= nr then
p := p + 1
goto nextPivot
end if
In M, swap row p with row (p + r) <-- bug. nr < p+r at this point
r := r + 1
end while
for 1 ≤ r < (nr - p) do
if M[p + r, p] != 0 then
x := -M[p + r, p] / M[p, p]
for p ≤ c < nc do
M[p + r, c] := M[p, c] * x + M[p + r, c]
end for
end if
end for
p := p + 1
end while
end function

 

[EtherealMystic]

That's alright. Hopefully someone else would be able to help.

 

[EtherealMystic]

... That coding just went over the top of my head. LOL

 

[oakpope]

there is plenty of help on Internet, just google reduced row echelon matrix

 

[star-warrior]

How to Change a Matrix to its Echelon Forms