In Exercises 21 and 22, mark each statement True or False. Justify each answer.a. A subspace of is any set H such that (i) the zero vector is in H; (ii) u; v; and u + v are in H, and (iii) is a scalar and cu is in H.b. If is the same as the column space of the matrix .c. The set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of .d. The columns of an invertible n × n matrix form a basis for .e. Row operations do not affect linear dependence relations among the columns of a matrix.

Book Chapter 1 All books in the new testament were written by Roman Christians. To understand the New Testament, we really need to know about three different worlds: o Christian World o Jewish World o Roman World Second Temple Period o The Persian Period o Synagogues emerged as significant sites for worshipping and teaching o Ruled by high priests with minimal inference from the Persian kings o The Hellenistic Period o A reign of terror o Antiochus IV Epiphanes sought to exterminate the Jewish religion by inflicting horrible atrocities upon anyone practicing the faith o The Hasmonean Period o Jewish rebels who led a successful revolt against Antiochus