Question

In: Math

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

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

Solutions

Expert Solution

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 )


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