Column Space of a Matrix Explained | Linear Algebra

We introduce the column space of a matrix, which is the span of the column vectors. If A is an mxn matrix, the span of the column vectors is a subspace of R^m, and again this is called the column space of the matrix A. We prove that the column space is a subspace of R^m, we prove the theorem stating Ax=b is consistent if and only if b is in the column space of A, we solve two problems determining if Ax=b is consistent and if b is in the column space of A, and finish by going over how to find a basis for a column space. #linearalgebra
Gauss-Jordan Elimination: • Guide to Gauss-Jordan ...
Find Basis for the Column Space: • Finding Basis for the ...
Row Vectors and Column Vectors: • Row Vectors and Column...
Row Space of a Matrix: (Coming soon)
0:00 Definition of Column Space and Intro
0:59 Proof Column Space is a Subspace of R^m
3:22 Ax=b if b is in the Column Space of A
6:40 Determine if Ax=b is consistent and if so write b as a Linear Combination of the Columns of A
10:11 Finding a Basis for the Column Space
Linear Algebra course: • Linear Algebra
Linear Algebra exercises: • Linear Algebra Exercises
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