.PROBLEM 2: Find the inverse of the coefficient matrix and use it to solve the system. -2x3 + 3x4 = 15 X3 + 6x4 = 5 -2x1 + x₂ = 1 -7x1 + 3x₂ 3 PROBLEM 3: Consider the set a 0 S=[A€M. (R) S=AEM3x2 (R): A=0 b, where a > 0, b>0, c>0 with the 0 с > 0 w² usual matrix addition and matrix scalar multiplication. a) Give an example of an element in S. b) Show that S is closed under addition or give an example to show that it's not. c) Show that S is closed under scalar multiplication or give an example to show that it's not. d) Find a basis for S. Make sure to verify the requirements for a basis. e) Find dim[S].