Solving for X inside of a 3X3Matrix

  • Thread starter Thread starter smashbrohamme
  • Start date Start date
AI Thread Summary
The discussion focuses on solving a system of equations using Cramer's rule within a 3x3 matrix framework. The initial setup leads to the equation x(2x-3)-1(2)+2(1)=-4x, which simplifies to 2x^2+x=0. A mistake is identified in the division step, where the incorrect result of 2x^2+1x=0 is derived. The correct solutions found are x=0 and x=-1, but the user expresses frustration over the error in their calculations. Ultimately, the thread highlights the importance of careful manipulation of equations in matrix algebra.
smashbrohamme
Messages
97
Reaction score
1
Using cramers rule.

the equation is.

x,1,2
1,x,3 all set to equal -4x
0,1,2


I made my 2x2 matrix like this

x|x,3| -1|1,3| +2|1,x|
|1,2| |0,2| |0,1|

eventually I ended up with x(2x-3)-1(2)+2(1)=-4x

condensed it down to 2x^2-3x=-4x

2x^2+1x=0
x(x+1)=0

x=0, or x=-1.

I go back to plug it in...and its wrong! :(
 
Physics news on Phys.org
When you had your initial equation, 2x^2+x=0 and you divided by 2, you got an incorrect result.
 
smashbrohamme said:
2x^2+1x=0
x(x+1)=0

Little mistake in this step...
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Solve the given equation that involves fractional exponent
Replies
4
Views
2K
Solve the given problem involving: ##\tan^{-1} (2x+1)+ \tan^{-1} (2x-1)##
Replies
10
Views
1K
Show that if ##x>1##, ##\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-##
Replies
8
Views
2K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
Replies
10
Views
2K
Elementary algebra: find the value of x
Replies
6
Views
2K
Where Do the Graphs of |3x-2| and 1/x Intersect and Diverge?
Replies
4
Views
2K
Solve ##x^{\frac{-1}{2}}-2x^{\frac{1}{2}}+x^{\frac{2}{3}}=0##
Replies
24
Views
2K
Question about this technique for solving simultaneous equations
Replies
4
Views
1K
Are Complex Solutions Overlooked When Solving \(16x^4 = 81\) Directly?
Replies
5
Views
3K
Solve these simultaneous equations
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top