Four MBA students take the same six courses at graduate business school. Their final marks in these courses are recorded (out of 100) in the matrix M = [m] where Page 9 of 10 the final mark in course j for MBA student i ow - Coulum mij = (a) State the matrices C and Q such that (i) the entries in the product MQ are the overall average final marks for cach student and (ii) the entrics in the product CM are the overall average final marks for each course. (b) State the matrix R such that the entries in the product RM represent a 5% increase in the final grades for all students in all courses. (c) Suppose the marks in M are altered as follows: the final mark for each student in Course #2 is reduced by 3 points, the final mark for each student in Course #5 is increased by 5 points, and all other marks remain unchanged. State the matrix K so that the sum K+ M has entries that reflect the alteration of the marks as described above.

Give an example showing that the rank of the product of two matrices can be less than the rank of either matrix.

Perform elimination on the following system of equations: 2х + 5y - 4x + 2y = 0 - What values do you got for the pivots? The first pivot is 2 and the second pivot is What is the augmented matrix that corresponds to the original system of equations above? 5 6. -4 What result do you get from performing elimination on the augmented matrix? What are the solutions you obtain for x and y after performing back substitution? and y 1 X =

Let A be a 2 X 3 matrix, B be a 3 X 2 matrix and v be a 3 X 1 vector. Indicate the dimensions of the resulting matrices or indicate if such operation is undefined by writing u x u a. AB is b. (Av) is c. AB-¹ is d. BAT ^+^ is e. v+v¹ is X X X X X