Find the solution of the following system of equations using Gaussian elimination method and show the steps. x-y+z = 4 5x-y+z = 6 3x-y+5z= 5

Question

Find the solution of the following system of equations using Gaussian elimination method and show the steps. x-y+z = 4 5x-y+z = 6 3x-y+5z= 5
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Solution 1

Sure, let's solve the system of equations using Gaussian elimination method.

The system of equations is:

  1. x - y + z = 4
  2. 5x - y + z = 6
  3. 3x - y + 5z = 5

Step 1: Write the system of equations in matrix form. The augmented matrix is:

[ 1 -1  1 | 4 ]
[ 5 -1  1 | 6 ]
[ 3 -1  5 | 5 
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