If a 3 x 4 matrix can have independent columns?

[Spyder89]

Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows?

Thanks!

 

[VeeEight]

What is the definition of linear independence?
You need to be more specific

 

[Spyder89]

Hey I think I figured out the answer, thanks for replying though.

 

[VeeEight]

No problem, cheers.

 

[blue_raver22]

I can confirm that a 3x4 matrix can indeed have independent columns. This means that each column in the matrix contains unique and non-redundant information, and no column can be expressed as a linear combination of the others. In other words, the columns are not dependent on each other and can be considered independent.

On the other hand, a 3x4 matrix can also have independent rows. This means that each row contains unique and non-redundant information, and no row can be expressed as a linear combination of the others. Similar to independent columns, independent rows indicate that the rows are not dependent on each other and can be considered independent.

Overall, a matrix can have both independent columns and independent rows, as long as each column and row contains unique and non-redundant information. This is an important concept in linear algebra and can have significant implications in various scientific fields, such as data analysis and machine learning. I hope this helps clarify your understanding of independent columns and rows in a matrix.