Finding Basis for the Column Space of a Matrix | Linear Algebra

We use elementary row operations to reduce a matrix to row echelon form in order to find a basis for the column space. After completing this process, the columns containing the leading 1s correspond to column in the original matrix which form a basis for the column space, col(A). Thus, the number of row vectors that have those leading 1s, which is the rank of the matrix, is also the dimension of the column space, since each leading 1 indicates a column of the original matrix that is in the basis of the column space. Again, recall a basis for the column space is a set of linearly independent column vectors that span the column space. #linearalgebra #matrices

What is the Column Space of a Matrix:    • Column Space of a Matrix Explained | ...  
Find Rank of a Matrix:    • How to Find the Rank of a Matrix (wit...  
Finding Basis for the Row Space of a Matrix:    • Finding Basis for the Row Space of a ...  

Linear Algebra course:    • Linear Algebra  
Linear Algebra exercises:    • Linear Algebra Exercises  

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