If A is a non-zero 4 x 7-matrix, then possible values for nullity(A) are: (a) 6,5, 4, 3, 2 (b) 6, 5, 4, 3 (c) 7,6, 5, 4, 3 (d) 4, 3, 2, 1 O c O d O a O b

solve (c)

The table below shows the number of tickets sold for seats in the stalls (S), circle (C) and upper circle (U) of a theatre for a show on Monday night and Tuesday night. (a) S 285 (c) Monday с 268 U S 182 279 Tuesday с 275 U 177 Represent this information in the 2 x 3 matrix A, so that A₁₁ is the number of stalls tickets sold for Monday and A2,3 is the number of upper circle tickets sold for Tuesday. Ticket prices to sit in the stalls, circle and upper circle were $88, $119 and $78 respectively. (b) Represent the ticket price information in matrix B so that matrices A and B can be multiplied together to create a meaningful result. State the order in which matrices A and B must be multiplied together, and determine the result of this multiplication, matrix M. (d) State the night on which the value of ticket sales was highest and calculate by how much the sales on this night exceeded the other night.

3. Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where A = 4 -3 and B= -2 -6 4