Question

Consider matrices in R 3×5 . What is the maximum possible number of linearly independent column vectors?

Answer 1

In a 3x5 matrix, the maximum number of linearly independent column vectors is 5.

Step-by-step explanation:

In a matrix of size 3x5, the maximum possible number of linearly independent column vectors is equal to the number of columns, which is 5. Each column vector can be considered as a vector in 3-dimensional space, and since the maximum number of linearly independent vectors in 3-dimensional space is 3, that would be the limit.

Answer 2

if a matrix 3 x 5 it does not imply that the column vector are linearly independent.

Step-by-step explanation:

A 3 x 5 matrix represents a linear map
`R^5 to R^3`. we have 5 columns vectors of
`R^3`. they can never be linearly independent because the dimension of
`R^3` is 3.