8. Let V be a finite dimensional vector space over R, with a positive definite scalar product. Let {e,.,e,} be an orthonormal basis for V. Let v, w eV. Let [v] =X and [w]=Y be their coordinate vectors...

Help with #8 please

= X ·Y; that is, the scalar product equals the dot product of X and Y. 9. Find a basis for the space of solutions for the homogeneous linear system AX = 0. Hint: Remember n = (n – r) + r, where r= rank A, and n –r is the number of parameters needed in the solution space. "/>
Extracted text: 8. Let V be a finite dimensional vector space over R, with a positive definite scalar product. Let {e,.,e,} be an orthonormal basis for V. Let v, w eV. Let [v] =X and [w]=Y be their coordinate vectors in R" with respect to this basis. Prove: = X ·Y; that is, the scalar product equals the dot product of X and Y. 9. Find a basis for the space of solutions for the homogeneous linear system AX = 0. Hint: Remember n = (n – r) + r, where r= rank A, and n –r is the number of parameters needed in the solution space.