Solve the following system of equations using matrices row o

Solve the following system of equations using matrices (row operations). If the system has no x + y - z = 4 3x - 4y + 10z = -15 x + 3y - 4z = 11 Select the correct choice below and, if necessary, fill in the answer box(es) in your choice. the solution is (Simplify your answers.) There are infinitely many solutions. the solution can be written as {(x, y, z) | x = y = (Simplify your answers. Type expressions using z as the variable.) There are infinitely many solutions. the solution can be written as {(x, y, z) | x = y is an) (Simplify your answer. Type an expression using y and z as the variables.) the system is inconsistent.

Solution

The augmented matrix of the given linear system is A =

1

4

-1

-3

3

-8

1

-10

-3

4

-5

5

We will reduce A to its RREF as under:

Add -3 times the 1st row to the 2nd row

Add 3 times the 1st row to the 3rd row

Multiply the 2nd row by -1/20

Add -16 times the 2nd row to the 3rd row

Multiply the 3rd row by -5/24

Add 1/5 times the 3rd row to the 2nd row

Add 1 times the 3rd row to the 1st row

Add -4 times the 2nd row to the 1st row

Then the RREF of A is

1

0

0

-3

0

1

0

1/4

0

0

1

1

Thus, the given linear system is equivalent to x = -3, y = ¼ and z= 1, so that the solution is (x,y,z) = (-3,1/4,1). Option A.

1	4	-1	-3
3	-8	1	-10
-3	4	-5	5