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- Define Vector Space and Vector subspace with the help of real time examples?Find a basis for the space of all 2 by 3 matrices whose columns add to zero. Find a basis for the subspace whose rows also add to zero.The set of all 2X2 matrices with ones on it's main diagonal is a subspace of R2x2 . true or false
- We denote the subspace spanned by the first two columns of A by U, and the subspace spanned by the last three columns of A by V . It's asked to determine a basis of U ∩ V, Please do it step by step, I got to the point of determining the null space which is (1/3, -1/3, 1, 1, 1)x5, but what happens after that?Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1)(2) On the plane determined by (1, 2, 1) and (1, −1, 1)(3) On the subspace spanned by (1, 2, 1), (1, −1, 1) and (3, 0, −3)Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector space?