Matrix help!

[MoriahBeee]

Solve the system of linear equations..

-x+2y+z-3w=3
3x-4y+z+w=9
-x-y+z+w=0
2x+y+4z-2w=3

I chose to Solve using Gaussian Elimination...

	-1	2	1	-3	3
	3	-4	1	1	9
	-1	-1	1	1	0
R4+2R3	2	1	4	-2	3

	-1	2	1	-3	3
	3	-4	1	1	9
R3-R1	-1	-1	1	1	0
	0	-1	6	0	3

​

	-1	2	1	-3	3
R2+2R1	3	-4	1	1	9
	0	-3	0	4	-3
	0	-1	6	0	3

	1	2	1	-3	3
	1	0	3	-5	18
	0	-3	0	4	-3
R4-1/3R3	0	-1	6	0	3

	1	2	1	-3	3
	1	0	3	-5	18
-1/3R3	0	-3	0	4	-3
	0	0	6	-4/3	4

	1	2	1	-3	3
	1	0	3	-5	18
	0	1	0	-4/3	1
1/6R4	0	0	6	-4/3	4

1	2	1	-3	3
1	0	3	-5	18
0	1	0	-4/3	1
0	0	1	-2/9	2/3

<<<Final Matrix






I put it back into the corresponding system of equations...

x+2y+z-3w=3
x+3z-5w=18
y-4/3w=1
z-2/9w=2/3

I am not sure what i am supposed to do next, or if i even began the problem correctly considering this is a 4x5 Matrix.
I put the Matrix into my graphing calculator and got the solutions ..
x=0
y=-3
z=0
w=-3 So confused. Please help! Thank you.

 

[Deleted member 4993]

Solve the system of linear equations..

-x+2y+z-3w=3
3x-4y+z+w=9
-x-y+z+w=0
2x+y+4z-2w=3

I chose to Solve using Gaussian Elimination...

	-1	2	1	-3	3
	3	-4	1	1	9
	-1	-1	1	1	0
R4+2R3	2	1	4	-2	3

	-1	2	1	-3	3
	3	-4	1	1	9
R3-R1	-1	-1	1	1	0
	0	-1	6	0	3

​

	-1	2	1	-3	3
R2+2R1	3	-4	1	1	9
	0	-3	0	4	-3
	0	-1	6	0	3

Why not R2 +3R1

-1.....2.....1.....-3.....3
.0.....2......4....-8.....18
.0.....-3.....0.....4.....-3
.0.....-1.....6.....0.....3

then 1/2*R2

-1.....2.....1.....-3.....3
.0.....1......2....-4.....9
.0.....-3.....0.....4.....-3
.0.....-1.....6.....0.....3

then 3R2 + R3

-1.....2.....1.....-3.....3
.0.....1......2....-4.....9
.0.....0.....6.....-8.....24
.0.....-1.....6.....0.....3

then R2 + R4

-1.....2.....1.....-3.....3
.0.....1......2....-4.....9
.0.....0.....6.....-8.....24
.0.....0.....8.....-4.....12

then -8/6*R3 + R4

and so on ....

Finally your matrix should look like:

a.....b.....c.....d.....e
.0.....f......g....h.....k
.0.....0.....m....n.....p
.0.....0.....0.....r.....s

that means - now your equations are:

a*x + b*y + c*z + d*w = e............................(1)
f*y + g*z + h*w = k.....................................(2)
m*z + n*w = p.............................................(3)
r*w = s.......................................................(4)

from (4) you get:

w = s/r

use this value of "w" in equation #3 to solve for "z" ...... and so on.....

	1	2	1	-3	3
	1	0	3	-5	18
	0	-3	0	4	-3
R4-1/3R3	0	-1	6	0	3

	1	2	1	-3	3
	1	0	3	-5	18
-1/3R3	0	-3	0	4	-3
	0	0	6	-4/3	4

	1	2	1	-3	3
	1	0	3	-5	18
	0	1	0	-4/3	1
1/6R4	0	0	6	-4/3	4

1	2	1	-3	3
1	0	3	-5	18
0	1	0	-4/3	1
0	0	1	-2/9	2/3

<<<Final Matrix






I put it back into the corresponding system of equations...

x+2y+z-3w=3
x+3z-5w=18
y-4/3w=1
z-2/9w=2/3

I am not sure what i am supposed to do next, or if i even began the problem correctly considering this is a 4x5 Matrix.
I put the Matrix into my graphing calculator and got the solutions ..
x=0
y=-3
z=0
w=-3 So confused. Please help! Thank you.

.

 

[mmm4444bot]

I chose to Solve using Gaussian Elimination...

1	2	1	-3	3
1	0	3	-5	18
0	1	0	-4/3	1
0	0	1	-2/9	2/3

Final Matrix

Your matrix does not have the correct form.

The 1s should form a diagonal from upper left to lower right on the 4x4 coefficient matrix.

Look up "row echelon form" and "reduced row echelon form".

Cheers :cool: