okay, so I'm trying to figure out how to do this 3x3 matrix. I'm suppose to be finding the determent and using CRAMER'S RULE. Can someone please explain to me how to do this?
4x-y+z= -5
2x+2y+3z=10
5x-2y+6z=1
http://www.youtube.com/watch?v=taBHTo8sviM
first determinant calculator
http://www.wolframalpha.com/widgets/view.jsp?id=7fcb0a2c0f0f41d9f4454ac2d8ed7ad6
+4 -1 +1
+2 +2 +3
+5 -2 +6
determinant = D = 55
Now for x put right side in x column
+5 -1 +1
10 +2 +3
+1 -2 +6
determinant = Dx = 125
x = 125/55
You go ahead and do y and z
Utube on how to find determinant of 3x3
http://www.youtube.com/watch?v=ROFcVgehEYA&feature=related
Now for x put right side in x column
-5 -1 +1 nope negative 5
10 +2 +3
+1 -2 +6
determinant = Dx = -55
x = -55/55
x = -1
You go ahead and do y and z
Sure, I can help you with that! To find the determinant and apply Cramer's rule to solve the system of equations, you need to follow a step-by-step approach. Let's break it down:
Step 1: Write the system of equations in matrix form. In this case, we have:
| 4 -1 1 | | x | | -5 |
| 2 2 3 | x | y | = | 10 |
| 5 -2 6 | | z | | 1 |
Step 2: Find the determinant of the coefficient matrix. To find the determinant of a 3x3 matrix, you can use the formula:
det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
In our case, the coefficient matrix A is:
| 4 -1 1 |
| 2 2 3 |
| 5 -2 6 |
You can substitute the values into the formula and calculate the determinant.
Step 3: Calculate the determinants of the matrices derived from replacing one column of the coefficient matrix with the constant vector. These determinants will be used to find the values of x, y, and z.
To find the determinant of the matrix obtained by replacing the first column (the x-coefficient column) with the constants vector, you get:
| -5 -1 1 |
| 10 2 3 |
| 1 -2 6 |
To find the determinant of the matrix obtained by replacing the second column (the y-coefficient column) with the constants vector, you get:
| 4 -5 1 |
| 2 10 3 |
| 5 1 6 |
To find the determinant of the matrix obtained by replacing the third column (the z-coefficient column) with the constants vector, you get:
| 4 -1 -5 |
| 2 2 10 |
| 5 -2 1 |
Step 4: Once you have the determinants for each case, use Cramer's rule to solve for x, y, and z.
The solutions will be:
x = det(Ax) / det(A)
y = det(Ay) / det(A)
z = det(Az) / det(A)
Substitute the determinants you calculated earlier into the formula and solve for x, y, and z.
And that's how you can solve the system of equations using Cramer's rule and find the determinant of a 3x3 matrix.