67. true or false: determine whether each statement is true or false, and briefly explain your answer by citing a theorem, providing a counterexample, or a convincing argument a. if a is a 7 x 4 matrix, then a can have rank 5 b. if.4 is a 4 x 7 matrix, then .4 can have nullity 5. c. if a is a 7 x 4 matrix, then a can have nullity 5. d. if a is a 7 x 4 matrix, then rank(a) +nullity(a) -7. e. if.4 is a 6 × 8 full rank matrix, then nullity(a)-2. f. ifa is a 5 x 8 full-rank matrix, then ab is always consistent for any b e r g. if.4 is a 5 × 8 full-rank matrix, then a b always has a unique solution for any b e r5. 140 section 1.8 the fundamental matrix spaces h. alb is consistent for some b er, then this systenm if a is a 7 x 5 full-rank matrix, and has a unique solution if.4 is a 7 × 5 full-rank matrix. aid | '4b | is consistent for some b e r 7, then | ald | ? s consistent for any other d e r' if.4 is a 7 × 5 full-rank matrix, then | a b always has a unique solution for any b e r/ if.4 is a 7 × 7 full-rank matrix, then a b always has a unique solution for any b e r 7. if ? s a 6 x 8 full-rank matrix, then | alb | always has an infinite number of solutions for i. j. k. l. if.4 is a 5x8 matrix, then [ab]? s always consistent for any b r 5. m. e if a is a 5 × 8 matrix, and | ? b | is consistent for some b r5, then | ald | 1s consistent for any otherde r ifa 1s a 7 × 5 matrix, then | alb | always has a unique solution for any b e r n. o.