Solving a matrix

Question

solve using a matrix 

 

x+2y-3z=-15

2x-3y+4z=18

-3+y+z=1

Answer 1

R1: 1   2  -3  -15 <--multiply by 4

R2: 2  -3   4   18 <--multiply by 3

R3: -3   1   1   1

 

R1:  4   8  -12  -60

R2:  6  -9   12   54 <--add R1+R2
R3: -3   1     1    1

 

R1:   1   2  -3  -15 
R2: 10  -1   0    -6   
R3: -3    1   1     1 <--multiply by 3

 

R1:   1  2 -3 -15
R2: 10 -1  0  -6
R3: -9   3  3   3 <--add R1+R3

 

R1:   1  2 -3 -15
R2: 10 -1  0   -6 <--multiply by 5
R3:  -8  5  0 -12 

 

R1:   1  2 -3 -15
R2: 50 -5  0 -30 

R3:  -8  5  0 -12 <--add R2+R3

 

R1:   1  2 -3 -15
R2: 50 -5  0 -30 <--divide row by 5
R3: 42  0  0 -42 <--divide row by 42

 

R1:   1  2 -3 -15
R2: 10 -1  0   -6 
R3:   1  0  0   -1 <--multiply by -10 and add resulting equation to R2

 

R1: 1  2 -3  -15
R2: 0 -1  0     4 
R3: 1  0  0    -1 <--multiply by -1 and add to R1

 

R1: 0  2 -3 -14 
R2: 0 -1  0    4 <--multiply by 2 and add to R1
R3: 1  0  0   -1

 

R1: 0  0 -3  -6 <--divide by -3
R2: 0 -1  0   4 <--divide by -1
R3: 1  0  0  -1

 

R1: 0 0 1  2 <-- same as z = 2
R2: 0 1 0 -4 <-- same as y = -4
R3: 1 0 0 -1 <-- same as x = -1