How can we know that for same eigen values how many eigen vectors are possible??

please solve this question

https://youtu.be/rNosSJudzco

not orthogonal

please prove orthogonality relation for these eigen vectors for same eigen value

we have infinite eigen vectors satisfying the condition of the vector

by n-r formula where n is order of matrix and r is rank of matrix , so by n-r we can find the number of linearly independent eigenvectors for same eigenvalues

dear it depends on condition or situation. for same eigen value eigen vectors may be different or may be same

infinity Eigen vectors can be possible but only those eigen vectors are valid which are orthogonal to each other .