How do you find the basis for the column space of a matrix?

Md Ariful Islam

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Dr. Md Rushad Rahman

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Row reduce the matrix and pick the columns that have pivot points. Let us use the matrix A: 1 3 5, 5 6 7, 10 12 14. If we now reduce it, we get the following matrix: 1 0 -1, 0 1 2, 0 0 0. The first two columns have pivot positions, but the last column does not. So we go back to the original matrix A and the first two columns of the original matrix A form the basis of the column space.

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