Question

Solve the following system of equations using matrices(row operations). If the system has no solution, say that it is inconsistent.

x - 3y + 4z = 10

2x + y + z = 6

-3 + 4y - 2z =. -15

Answer 1

The given system of equation can be written as a matrix form as

   =

A X = B where A = , X = and B =

Let us solve this equation by Matrix Rank method.

The augmented matrix is

Then the matrix form be

=  

=

Comparing each and every entry yields

Third entry gives 7z = 7 implies z = 7/7 = 1

Second entry gives 7y -7z = -14 implies 7y -7(1) = -14  

7y = -14+7 = -7 . Thus, y = -7/7 = -1

First entry gives x -3y +4z = 10 implies x -3(-1) +4(1) = 10

x = 10-3-4 = 10-7 = 3

Hence, the solution set (x, y, z) = ( 3 , -1 , 1 )