SOLUTION: I have tried every solution and I cannot come up with an answer to this problem.
I am trying to solve the problem by Crammer's Rule using determinants. The problem is: 3x - 2y+ z
Algebra.Com
Question 136905: I have tried every solution and I cannot come up with an answer to this problem.
I am trying to solve the problem by Crammer's Rule using determinants. The problem is: 3x - 2y+ z = 6
4x -4y + 3z = 0
5x - 4y + z = -5
I would very much appreciate your help,I have spent hours trying to find solutions to this problem. Thank-you.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve the problem by Cramer's Rule using determinants. The problem is:
3x - 2y+ z = 6
4x -4y + 3z = 0
5x - 4y + z = -5
-------------------------
The determinant of the coefficients is:
[-12-16-30]-[-20-36-8] = -58--64 = 6
-------------------------
Replace the "x-column" with the constant column to get:
6...-2...1
0...-4...3
-5..-4...1
------------
The determinant of that 3 x 3 matrix is:
[-24+0+30)-(20+-72+0) = 6--52= 58
---------------------
Divide the x-determinant by the coefficient determinant to get x = 58/6=29/3
-------------------
To find "y":
1st:Replace the "y-column" in the coefficient matrix by the constant column.
2nd:Find the determinant of this matrix
3rd:Divide that value by 6 to get the value of "y".
---------------------
Follow the same pattern for "z".
---------------------
Final answer:
x = 29/6
y = 91/6
z = 44/6
==============
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Step 1: Create the coefficient determinant and the answer column matrix
Step 2: Evaluate the determinant.
Step 3: Now, take the coefficient determinant and replace the x-column (the first column) with the answer column, like this:
Step 4: Evaluate the determinant as shown in step 2.
Cramer's rule states that
Step 5: Repeat step 3 and 4, except replace the y-column (the second column) with the answer column matrix and apply Cramer's rule:
Step 6: Do it one more time replacing the z-column (the third column) with the answer column.
Hint: Be extremely meticulous about the signs on the numbers when evaluating the determinants. If you have access to Microsoft Excel, you can put the coefficients into a square set of cells, one coefficient per cell. Let's say you put them in cells A1 through C3, then in an empty cell, type in =MDETERM(A1:C3). When you hit enter, the value of the determinant will appear.
RELATED QUESTIONS
I need help with this problem I have tried and number of different ways to solve it and I (answered by longjonsilver)
I need some help with this problem. I have tried to work it and cannot seem to come up... (answered by ankor@dixie-net.com,mangopeeler07)
I have one more equation that I am having problems with. Once again, the answer I came... (answered by dolly)
I am trying to solve and find the solution by using the elimination method. I have tried... (answered by Alan3354)
I am having a hard time figuring this out and I cannot come up with any possible solution (answered by stanbon)
I have made many attempts to answer this equation and cannot come up with the answer -... (answered by stanbon)
(((A cyclist traveled at a rate of 32 MPH to visit a nearby town. The cyclist averaged... (answered by stanbon)
How much pure water must be mixed with 6 pints of 60% developer to produce a mixture that (answered by richwmiller)
I am trying to solve a linear equation with three variables and I am stuck on this... (answered by KMST)