Question

How to find basis of 3x3 matrices vector space?

Answer 1

first u turn ur matrix into system of equations, and u check for linear independence, and if that the set spans the vector space. then what ever u get as ur linearly independent matrix, its ur basis for that vector space

Answer 2

but I'm asked to find the basis of \[M_{3\times3}(R)\] in general.

Answer 3

the natural basis for matrix 0f 3by3 matrix is linearly independent and span 3by3 matrix,