  # I do not understand Matrices and the Gauss Jordan method of elimination. Is there an easy way to know what to divide or multiply by to get to 0;s and 1's most efficiently?

Question

I do not understand Matrices and the Gauss Jordan method of elimination. Is there an easy way to know what to divide or multiply by to get to 0;s and 1's most efficiently?

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Step 1

Guass jordan method of elimination is used to solve the system of equations. By writing the system of equations in the form of augmented matrix and then perform row operations to write the matrix in the form of identity matrix where all the elements in principal diagonal are 1 and rest all are 0. then we get solution of x,y,z.

Let us consider an example and will discuss steps to follow to solve the system of equations using gauss jordan method.

The system of equations be

x+y+z = 4, 3x+4y+2z=4, x-3y-2z = 8

Step 2

Here there are three system of equations with three variables. We use Guass jordan method to solve the equations.

To write the augmented matrix we write the coefficients of x,y,z of first equation in first row of matrix, coefficients of xy,z of second equation in second row of matrix, coefficients of x,y,z of thrid equation in third row of matrix separated by a line and writing the constants on other side of line respectively.

The augmented matrix of given system of equations looks like below.

Step 3

Now we perform row operations to convert the matrix into identity matrix with 1 in principal diagonal and rest all 0.

FIrst let us go from column to column.

1. Check if first element in first column is 1 or not. If not then run a row operation to make it 1 and then perform row operations to make second element and third element in first column to 0.

2. Check if second element in second column is 1 or not. If not then run a row...

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