Question

Solve the system

-2x1+4x2+5x3=-22

-4x1+4x2-3x3=-28

4x1-4x2+3x3=30

a)the initial matrix is:

b)First, perform the Row Operation 1/-2R1->R1. The resulting matrix is:

c)Next perform operations

+4R1+R2->R2

-4R1+R3->R3

The resulting matrix is:

d) Finish simplyfying the augmented mantrix down to reduced row echelon form. The reduced matrix is:

e) How many solutions does the system have?

f) What are the solutions to the system?

x1 =

x2 =

x3 =

Answer 1

(a) The augmented matrix for the given system of equation is as follows,

(b) First, perform the Row Operation 1/-2R1->R1. The resulting matrix is:

(c) Next perform operations

+4R1+R2->R2

-4R1+R3->R3

The resulting matrix is:

(D) Divide R2 by -4 so we get,

Multiply R2 by 2 and add with R1

Now multiply R2 by 4 and subtract it from R3 to get R3

(e) Since for last row we get 0 = 2 as result, which is not possible.

So there is no solution to this system of equation.

(f) Since the system has no solution we cannot find the value of x1, x2, x3

.