Solving a question using cramer rule

Question

3x - 2y + 5z = 6

 

9x - 8y + 1z = 46

 

-6x - 4y + 7z = 27

Answer 1

When using Cramer's rule, you will take the determinant.  To find the determinant, we convert the system of equations into a matrix.

 

When forming the matrix, you will have a column of coefficients that correspond to the variables.  The lowest variable is the first column.  So here is our matrix.  Call this matrix M.

 

3         -2           5

 

9         -8           1

 

-6        -4           7

 

 

Then find the determinant of this matrix.  That is det(M).

 

Next, you will find the determinant for each column.

 

Find det(x) using the matrix

 

 

6        -2         5

 

46      -8         1

 

27      -4         7

 

 

 

Then find det(y) using the matrix

 

3        6         5

 

9        46       1

 

-6       27       7

 

 

Then find det(z) using the matrix

 

3         -2           6
 
9         -8           46
 
-6        -4           27

 

 

Notice that in the last three matrices, the coefficients on the right side of the equation correspond to the columns of the specific determinants.

 

So now your solutions are

 

x = det(x) / det(M)

 

y = det(y) / det(M)

 

z = det(z) / det(M)