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    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.