1. The problem statement, all variables and given/known data Suppose V1 (dim. n1) and V29dim. n2) are two vector subspaces such that any element in V1 is orthogonal to any element in V2.Show that the dimensionality of V1+V2 is n1+n2 2. Relevant equations 3. The attempt at a solution The subspace V1 is spanned by n1 linearly indipendent (mutually orthogonal) vectors. The subspace V2 is spanned by n2 linearly indipendent (mutually orthogonal) vectors. Also, the space V1+V2 is spanned by (n1+n2) mutuallyorthogonal vectors.Since, any element in V1 is perpendicular to any element in V2.Thus,the space will be spanned by (n1+n2) linearly independent vectors. Clearly, the dimension will be n1+n2. Please tell me if there is a fault in my argument.