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

What is subspace of a vector space and define Linear Transformation. Give one example for each

The subspaces of R3 are planes, lines, R3 itself, or Z containing only (0, 0, 0).(a) Describe the three types of subspaces of R2 .(b) Describe all subspaces of D, the space of 2 by 2 diagonal matrices.

Check which of the subsets below are M2x2 subspaces with operations usual.   (a) The set of all matrices A2x2 such that det (A) = 0.

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)

If V is the subspace spanned by (1, 1, 1) and (2, 1, 0), find a matrix A that has Vas its row space. Find a matrix B that has Vas its nullspace. Multiply AB.