Thread: I need major help :(

1. I need major help :(

Questions can be found here:
http://www.freewebs.com/kgpretty/math.JPG

I attempted #4.. can you use 4 .. determinants? to solve the equation like:
Code:
x|k  l|  -a|l  m|   x|k  l|   -a|l  m|
|m  n|    |n  o|    |o  k|     |n  o|
For #7, I've think I've got that covered. Just tell me.. would the augmented matrix be:
|log1 log1 log1|0|
to represent the first row?

or |1 1 1|0|, where log is factorised out?

For all the other questions.. I simply don't know what to do

2. Originally Posted by kgpretty

I attempted #4..
No only 3.
Expand along the first row:
Code:
x [x b]-a[a b]+b[a x]
[b x]   [a x]    [a b]   =0

Do my excersice.
Show that the determinant below is always zero.
----
Once you have done that you can use the fact, x,y,z>0
log(2x)=log2 +log x
log(2y)=log2 +log y
log(2z)=log2 +log z
log(3x)=log3+log x
log(3y)=log3+log y
log(3z)=log3+log z
Let,
a=log x
b=log y
c=log z
Then you end with,
Code:
a                b            c
a+log 2  b+log 2  c+log 2
a+log 3  b+log 3  c+log 3
Then use that result.

4. Originally Posted by ThePerfectHacker
No only 3.
Expand along the first row:
Code:
x [x b]-a[a b]+b[a x]
[b x]   [a x]    [a b]   =0
When I expand along the first row, the result isn't equal to 1.
From the first expansion, you get:
x^3 - b^2x

There's no x^3 in the other expansions to cancel the x^3 already there. How can I be equal to 0?

5. Originally Posted by kgpretty
When I expand along the first row, the result isn't equal to 1.
From the first expansion, you get:
x^3 - b^2x

There's no x^3 in the other expansions to cancel the x^3 already there. How can I be equal to 0?
Expand it each determinant.
x(x^2-b^2)-a(ax-ab)+b(ab-ax)=0
Thus,
x^3-xb^2-a^2x+a^2b+ab^2-abx=0
Thus,
x^3-x(b^2-ab+a^2)+a^2b+ab^2=0

6. Originally Posted by ThePerfectHacker
Expand it each determinant.
x(x^2-b^2)-a(ax-ab)+b(ab-ax)=0
Thus,
x^3-xb^2-a^2x+a^2b+ab^2-abx=0
Thus,
x^3-x(b^2-ab+a^2)+a^2b+ab^2=0
I'm sorry, I don't get it.
How does x^3-x(b^2-ab+a^2)+a^2b+ab^2 equal to 0?

7. Originally Posted by kgpretty
I'm sorry, I don't get it.
How does x^3-x(b^2-ab+a^2)+a^2b+ab^2 equal to 0?
Because the left hand side (determiant) was expaned into this equation. Now the problem says to solve when it is equal to zero.