Showing that linear independence of pivot columns implies linear independence of the corresponding columns in the original equation Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/showing-that-the-candidate-basis-does-span-c-a?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/dimension-of-the-column-space-or-rank?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. ... https://www.youtube.com/watch?v=BfVjTOjvI30 Note: All Khan Academy content is available for free at (www.khanacademy.org)

Let's practice some two step equations, some of which require merging terms and using the distributive property. Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/e/linear_equations_2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Watch the next lesson: https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/solving-equations-1?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Missed the previous lesson? https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/equations_beginner/v/equations-2?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI ... https://www.youtube.com/watch?v=tuVd355R-OQ Note: All Khan Academy content is available for free at (www.khanacademy.org)