Linear Algebra Example Problems – Matrix Column Space Basis and Dimension

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The column space of a matrix consists of all linear combinations of the matrices columns. In this video we show how to to find a basis to describe this subspace.

Simply perform row operations on A to obtain a reduced echelon form of the matrix. Identify the pivots in the reduced matrix. For each pivot location, grab the corresponding column in the original matrix. This collection of columns forms a basis for col(A) and the number of vectors/pivots is the dimension of the space.

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