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#### Question

Express the following equations in the matrix form and solve them by method of reduction :

2x- y + z = 1, x + 2y + 3z = 8, 3x + y - 4z =1

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The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices.

Find the inverse of the matrix, `A=[[1,3,3],[1,4,3],[1,3,4]]`

by using column transformations.

Solve the following equations by the method of reduction :

2x-y + z=1, x + 2y +3z = 8, 3x + y-4z=1.

The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.

Using elementary transformations, find the inverse of the matrix A = `((8,4,3),(2,1,1),(1,2,2))`and use it to solve the following system of linear equations :

8*x* + 4*y* + 3*z* = 19

2*x* + *y* + *z* = 5*x* + 2*y* + 2*z* = 7