Question 1037171
(a) The system 
2x + 3y = 1
5x + 9y = 4
is equivalent to the matrix equation

{{{(matrix(2,2,2,3,5,9))*(matrix(2,1,x,y)) = (matrix(2,1,1,4))}}}, with {{{A = (matrix(2,2,2,3,5,9))}}}


(b) The matrix {{{A = (matrix(2,2,2,3,5,9))}}} is nonsingular since its determinant is {{{18 - 15 = 3 <> 0}}}.  Its inverse is given by {{{A^(-1) = (1/3)*(matrix(2,2,9,-3,-5,2))}}}


(c) {{{(matrix(2,1,x,y))}}}= {{{(1/3)*(matrix(2,2,9,-3,-5,2))*(matrix(2,1,1,4))}}} = {{{(matrix(2,1,-1,1))}}}, after left-multiplying both sides of the equation by {{{A^(-1)}}} and simplifying.