Matrix with complex numbers: 2ix + y - z = -1 -x +3y +2z = 5 - 7i 3x + (1+iy) - iz =

[Isiltir]

I can't find solution to this matrix:

2ix + y - z = -1
-x +3y +2z = 5 - 7i
3x + (1+iy) - iz = 5 - 2i

First of all, it seems there is a mistake in the third equation: more logical would be (1+i)y.
However i did not find the solution using both versions.
I multiplied first equation by i and then added second one multiplied by (-1) to the first.

1 i-3 -i-2 = -5+6i
-1 3 2 = 5-7i
3 1+i -i = 5-2i

Then added first one to the second and also first one multiplied by (-3) to the third line.

1 i-3 -i-2 = -5+6i
0 i -i = -i
0 -2i+10 2i+6 = 20-20i

Multiply second by i and the third by 1/ -2i+10 and add second to third

1 i-3 -i-2 = -5+6i
0 -1 1 = 1
0 0 2i+6/-2i+10 = 20+20i/-2i+10

I got to 16z = 30 + 18i, but that doesn't seem to be right.

Is there a quick way to find solution?

 

[tkhunny]

I can't find solution to this matrix:

2ix + y - z = -1
-x +3y +2z = 5 - 7i
3x + (1+iy) - iz = 5 - 2i

First of all, it seems there is a mistake in the third equation: more logical would be (1+i)y.
However i did not find the solution using both versions.
I multiplied first equation by i and then added second one multiplied by (-1) to the first.

1 i-3 -i-2 = -5+6i
-1 3 2 = 5-7i
3 1+i -i = 5-2i

Then added first one to the second and also first one multiplied by (-3) to the third line.

1 i-3 -i-2 = -5+6i
0 i -i = -i
0 -2i+10 2i+6 = 20-20i

Multiply second by i and the third by 1/ -2i+10 and add second to third

1 i-3 -i-2 = -5+6i
0 -1 1 = 1
0 0 2i+6/-2i+10 = 20+20i/-2i+10

I got to 16z = 30 + 18i, but that doesn't seem to be right.

Is there a quick way to find solution?

"doesn't seem right" is a big red flag. Be more careful. Be more systematic.

1) 2i 1 -1 -1
2) -1 3 2 (5-7i)

Multiply #2 by 2i

1) 2i 1 -1 -1
2a) -2i 6i 4i (14+10i)

Add to get your new #1

1a) 0 (1+6i) (-1+4i) (13+10i)

One thing at a time. WRITE DOWN EVERYTHING.