Solve the system of equations using Cramer's rule?

Question

Solve the system of equations using Cramer's rule

x1 + 2x2 + x3 = 3
x1 + x2 - x3 = 4
2x1 - x2 + x3 = 5

Answer 1

Okay, what you need to do is create a coefficient matrix for your data. In this example, the matrix would look like this:

1 2 1
1 1 -1
2 -1 1

Now if you calculate the DETERMINANT of this, you'll get a value. We'll just call it det(A).

Cramer's rule says that you take each column of the matrix (one by one) and replace it with the column on the OTHER side of the equals sign. So you'll have THREE new matricies after doing this. We'll call them A1, A2, A3.

A1 =
3 2 1
4 1 -1
5 -1 1
(Note that we replaced column 1 in A with 3, 4 and 5 - the numbers on the right of the equals signs).

A2 =
1 3 1
1 4 -1
2 5 1

And

A3 =
1 2 3
1 1 4
2 -1 5

Again, you want to calculate the DETERMINANTS of these matrices. We'll call those det(A1), det(A2) and det(A3) respectively.

We can then calculate each of the variables using the following formulas:

x1 = det(A1) / det(A)
x2 = det(A2) / det(A)
x3 = det(A3) / det(A)

And that's it. Now if you need help calculating the determinants, email me at: [e-mail].

Hope that helps.

Answer 2

Cramers Rule is composed of determinants interior the numerator and denominators. The numerators variety for each variable, yet not the denominator. The denominator is | a million a million -a million| | 5 -a million a million| = a million(3 - 2) - a million(-15-a million) -a million(10+a million) increasing throughout the time of | a million 2 -3| row a million = a million + sixteen - eleven = 6 The numerator for x, which I write as X, is | -a million a million -a million| |-eleven -a million a million| basically the previous numbers, yet column one | 0 2 -3| makes use of the constants from the unique situation! = -a million(3 - 2) - a million(33-0) -a million(-22+0) increasing throughout the time of row a million = -a million -33 + 22 = -12 So x = -12/6 = -2. further, Y is | a million -a million -a million| | 5 -eleven a million| basically the previous numbers, yet column 2 | a million 0 -3| makes use of the constants from the unique situation! = a million(33-0)+a million(-15-a million)-a million(0+eleven) = 33 - sixteen -eleven = 6 So y= 6/6 = a million. finally, Z is | a million a million -a million| | 5 -a million -eleven| basically the previous numbers, yet column threee | a million 2 0| makes use of the constants from the unique situation! = a million(0+22)-a million(0+eleven)-a million(10+a million) = 22 - eleven - eleven = 0 So z= 0/6 = 0.

Answer 3

x1 = 3
x2 = 1/3
x3 = -2/3
I just can not place the solution. Cramer's rule is a long process

Answer 4

here is a web site for you

http://www.maths.surrey.ac.uk/explore/emmaspages/Matrix10.html

this give you the 3x3 determinant you need for Cramer's rule