Let S be the set of all real 2x2 matrices whose rows are orthogonal vectors. Show whether S is a subspace of Mat2x2 (R)

State the Fundamental Subspace Theorem and give an example of its application in the case of a 2 x2 matrix.

Show whether the set W of all diagonal 3 x 3 matrices is a subspace of M3x3 or not O O D

If U and W are subspaces of V such that V = U + W and Un W= {0}, then prove that every vector in V has a unique representation of the form u+ w where u is in U and w is in W. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). U Paragraph Arial 14px A

In linear algebra, does a basis for a subspace W always span W?  (True or False)