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## Main Question or Discussion Point

Hi all,

I have been studying Linear Algebra for an upcoming exam, and one question has puzzled me slightly! How do you determine of a vector in R4 is linearly independent?

Given three vectors, each with 4 rows, I know you are meant to arrange them into a matrix, like this:

[tex]\[ \left( \begin{array}{ccc}

a & e & i \\

b & f & j \\

c & g & k\\

d & h & l\end{array} \right)\]

[/tex]

In this case you are unable to find the determinant as it is not a square matrix. Are you meant to use row reduction instead? And if so, how do you ascertain whether it is independent or dependent? I'd appreciate any help clearing this up!

Cheers.

I have been studying Linear Algebra for an upcoming exam, and one question has puzzled me slightly! How do you determine of a vector in R4 is linearly independent?

Given three vectors, each with 4 rows, I know you are meant to arrange them into a matrix, like this:

[tex]\[ \left( \begin{array}{ccc}

a & e & i \\

b & f & j \\

c & g & k\\

d & h & l\end{array} \right)\]

[/tex]

In this case you are unable to find the determinant as it is not a square matrix. Are you meant to use row reduction instead? And if so, how do you ascertain whether it is independent or dependent? I'd appreciate any help clearing this up!

Cheers.