Thread: Matrix, rank

Hello!

If you have the matrix

1, 0, 1, -1
1, 1, 0, 1
1, 1, 0, 1

why ist he rank 2 and not 1? Couldn’t you make

1, 0, 1, -1
1, 1, 0, 1 / -line 3
1, 1, 0, 1 / -line 2
=
1, 0, 1, -1
0, 0, 0, 0
0, 0, 0, 0

I suppose the line operation is invalid, but why?

Thanks for your help

Schdero

Originally Posted by Schdero

Hello!

If you have the matrix

1, 0, 1, -1
1, 1, 0, 1
1, 1, 0, 1

why ist he rank 2 and not 1? Couldn’t you make

1, 0, 1, -1
1, 1, 0, 1 / -line 3
1, 1, 0, 1 / -line 2
=
1, 0, 1, -1
0, 0, 0, 0
0, 0, 0, 0

I suppose the line operation is invalid, but why?

Thanks for your help

Schdero

(1, 0, 1, -1) and (1, 1, 0, 1) are linearly independent. (Neither is a multiple of the other.) So, the rank is 2.

Originally Posted by Schdero

Hello!

If you have the matrix

1, 0, 1, -1
1, 1, 0, 1
1, 1, 0, 1

why ist he rank 2 and not 1? Couldn’t you make

1, 0, 1, -1
1, 1, 0, 1 / -line 3
1, 1, 0, 1 / -line 2
=
1, 0, 1, -1
0, 0, 0, 0
0, 0, 0, 0

I suppose the line operation is invalid, but why?

Thanks for your help

Schdero

This is like some board games: one operation per turn. If you substract the second line from the third then the third line's already

all zeroes, so substracting it now from the second line won't change anything, and this is why the matrix's rank is 2.

Tonio