Answer Happy

23. For each of the situations (a)–(f) below, decide which of the statements in the box can correctly complete the sentence. Include all correct responses. (a) If A is an 8 x11 matrix whose rank is 6, then (b) If A is an 8 x 11 matrix whose rank is 8, then (C) If A is an 8 x 11 matrix whose rank is 10, then (d) If A is a 12 x 7 matrix whose rank is 9, then (e) If A is a 12 x 7 matrix whose rank is 7, then (f) If A is a 12 x 7 matrix whose rank is 5, then (i) AX = b is solvable for every vector b. (ii) there are some vectors b for which AX = b is not solvable. (iii) for some vectors b, the system AX = b has exactly one solution. (iv) for some vectors b, the system AX = b has infinitely many solutions. (v) the given information is contradictory, no such system is possible.