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A determinant containing a variable

by Quark Itself
Tags: determinant, variable
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Quark Itself
#1
Jan15-13, 01:50 PM
P: 25
1. The problem statement, all variables and given/known data
I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants?
[x 2x 4 x ]
[1 2 2x 1 ]
[2x x-1 2 3x]
[ 2 x+1 x+3 x-1]
What are the different values of x?

2. Relevant equations



3. The attempt at a solution
I've tried ellimination and by using cofactors. When fully computed, it will be a polynomial of the 4th degree, as one probably can see.
Ellimination didn't make it simpler to factorize and cofactors just solved it until the polynomial popped up at the end-
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Mark44
#2
Jan15-13, 01:52 PM
Mentor
P: 21,258
Quote Quote by Quark Itself View Post
1. The problem statement, all variables and given/known data
I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants?
[x 2x 4 x ]
[1 2 2x 1 ]
[2x x-1 2 3x]
[ 2 x+1 x+3 x-1]
What are the different values of x?

2. Relevant equations



3. The attempt at a solution
I've tried ellimination and by using cofactors. When fully computed, it will be a polynomial of the 4th degree, as one probably can see.
Ellimination didn't make it simpler to factorize and cofactors just solved it until the polynomial popped up at the end-
What did you get?
Quark Itself
#3
Jan15-13, 02:04 PM
P: 25
8x4-22x3-22x2+47x+3

LCKurtz
#4
Jan15-13, 09:52 PM
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A determinant containing a variable

Quote Quote by Mark44 View Post
What did you get?
Quote Quote by Quark Itself View Post
1. The problem statement, all variables and given/known data
I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants?
[x 2x 4 x ]
[1 2 2x 1 ]
[2x x-1 2 3x]
[ 2 x+1 x+3 x-1]
What are the different values of x?
Quote Quote by Quark Itself View Post
8x4-22x3-22x2+47x+3
Is this your determinant?$$
\left|\begin{array}{cccc}
x & 2x & 4 & x \\
1 & 2 & 2x & 1\\
2x & x-1 & 2 & 3x\\
2 & x+1 & x+3 & x-1
\end{array}\right|$$
If so, your last two terms should be ##44x+12##. Still, once you have the polynomial correct, you haven't said what you are supposed to do with it. It doesn't make sense to ask "what are the different values of ##x##".
HallsofIvy
#5
Jan16-13, 07:58 AM
Math
Emeritus
Sci Advisor
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PF Gold
P: 39,497
Quote Quote by Quark Itself View Post
1. The problem statement, all variables and given/known data
I have this 4x4 determinant and usually these are just mechanical work, until I stumbled upon one containing x, how should one go about solving these type of determinants?
[x 2x 4 x ]
[1 2 2x 1 ]
[2x x-1 2 3x]
[ 2 x+1 x+3 x-1]
What are the different values of x?
The different values of x that give the determinant what property? That it be 0? That it not be 0?

2. Relevant equations



3. The attempt at a solution
I've tried ellimination and by using cofactors. When fully computed, it will be a polynomial of the 4th degree, as one probably can see.
Ellimination didn't make it simpler to factorize and cofactors just solved it until the polynomial popped up at the end-


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