Linear Algebra homework help.

[MetalMat]

Here is the question:

Is it possible to find a 3x2 matrix with orthonormal rows? Please help me explain this too.

I beleive a matrix with orthonormal rows has to be square, so I would say no as of right now.

 

[Gibson486]

orthonormal as in all vectors must be unit vectors and perpendicular to each other?

 

[KEV1N]

As far as I remember in order for a matrix to be orthonormal it has to be orthogonal and normal... to be orthogonal you have to be able to multiply the matrix by it's transposition and end up with the identity matrix (1's all down the diagonal and 0s elsewhere). I don't think you can do that with a matrix that isn't square, but then again it's been about 5 years?

 

[Goosemaster]

Orthonomals are unit vectors tha are perpendicular..IIRC, as someone said, it seems to be an identity matrix.

 

[ArmenK]

No, one of the rows would have to be linearly dependent on the other 2 rows. You are dealing with 2 dimensional vectors so the biggest number of linearly independent vectors (row Rank) you can get is 2.

 

[maziwanka]

if the columns have to be orthogonal to each other, then no, since you have 3, 2 dim vectors describing a 2 dim space. you have 1 too many columns.

 

[MetalMat]

Originally posted by: ArmenK
No, one of the rows would have to be linearly dependent on the other 2 rows. You are dealing with 2 dimensional vectors so the biggest number of linearly independent vectors (row Rank) you can get is 2.

Sounds good to me :thumbsup: