Motivation to study Change of Basis Matrix along with an example and homework problem

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Co-ordinate vector:

change of basis is one of the very important concept in Linear Algebra. If we have a coordinate vector of a vector with respect to one ordered basis and if we want to find a coordinate vector with respect to another ordered basis but its difficult to find so we take help of change of basis matrix.

change of basis is a matrix whose column vectors are the coordinate vectors.

[LokeshSharma-hmjz]

now i will not forget this concept . Thanks

[rahulkurup]

Awesome vedio and best explanation. Tried studying from nptel but my time got wasted and I found this vedio and I will never forget this concept now.
🙏Great personality sir🙏

[naobaangom]

Let S1={(1, -2), (3, -4)} and S2={(1, 3), (3, 8)} be two bases of R2. Then change of basis Matrix from S2 to S1. How to calculate sir please reply 🙏