Lin Alg: Invertible Change of Basis Matrix

[YoshuaV]

king



[twotalkingmimes]

Used this for an assignment today. Thanks a lot!

[villagehomeboy]

question: Isn't C always going to be invertible since it is a basis? And by definition, isn't a basis a set of linearly independent vectors? So by this reasoning, we can solve for [a]b by solving for the system of equations (your previous video) but also taking the inverse of C (the current video)?

by the way, these videos are very helpful. Thank you.

[omgthatscrazyx]

@villagehomeboy I don't believe so because you could have 3 linearly independent vectors that have 4 components, but only span R^3. which would be a 4x3 matrix which you cannot invert.

[Waranle]

Thank you Sal