# Vectors and Linear Algebra : Basis, Column Space and Rank

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2 1 -1 3 4

1 0 -1 2 0

A= 1 1 0 1 4

4 2 -2 6 8

Find the basis for the row space, column space of A; What is the rank of A?

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#### Solution Preview

Well, the matrix is:

The number of pivot columns in the rref(A) shows the number of linearly independent columns and if we pick the corresponding columns, they will form a basis for the column space of the given matrix. Therefore, we must find rref(A) using elementary row/column operations and we get:

Well, only the first and second columns are the ...

#### Solution Summary

Basis, column space and rank are found for a matrix.

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