Please provide clear workings for the equations below.

Problem Set A 1. Given the following matrix: Determine answers to the following: a. State the dimensions of the matrix. [1 mark] b. If cofactor;; (Ci3) is equal to 36, calculate the value of the element;s (a;3). [4 marks] c. Using your answers from part b. above, calculate the matrix that will be derived from the expression 2F + %D, where D = F * 415. [6 marks] d. After completing Part c. above, state the name of the resultant matrix. [1 mark] 2. Matrix A below is a singular matrix, calculate the value(s) of q. [5S marks] _[a ] 4 [3 2q 3. Three hundred and sixty-eight (368) students of The UWI Global Campus are registered to do ECON1003. The ethnicity of the registered students is Black, East Indian and Latino. If there are four times as many East Indian students as there are twice as many Black students plus Latino students and thrice as many East Indian students as there are four hundred and ninety- one students minus twice as many Latino students. a. State three variables to represent the events presented in the above information. [1 mark] b. Write three linear equations to represent the above information. [2 marks] c. Using your answer from part b. above, write the linear equations in matrix form. [2 marks]