SOLUTION: Consider the following system of equations:  2x + 3y = 1 5x + 9y = 4 (a) Write the system of equations as a matrix equation AX = B. (b) Calculate A −1 . (c) Solve

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Consider the following system of equations:  2x + 3y = 1 5x + 9y = 4 (a) Write the system of equations as a matrix equation AX = B. (b) Calculate A −1 . (c) Solve       Log On


   

Question 1037171: Consider the following system of equations:

2x + 3y = 1
5x + 9y = 4
(a) Write the system of equations as a matrix equation AX = B.
(b) Calculate A
−1
.
(c) Solve AX = B using your result from part (b).
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(a) The system
2x + 3y = 1
5x + 9y = 4
is equivalent to the matrix equation
, with A+=+%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29

(b) The matrix A+=+%28matrix%282%2C2%2C2%2C3%2C5%2C9%29%29 is nonsingular since its determinant is 18+-+15+=+3+%3C%3E+0. Its inverse is given by A%5E%28-1%29+=+%281%2F3%29%2A%28matrix%282%2C2%2C9%2C-3%2C-5%2C2%29%29

(c) %28matrix%282%2C1%2Cx%2Cy%29%29= %281%2F3%29%2A%28matrix%282%2C2%2C9%2C-3%2C-5%2C2%29%29%2A%28matrix%282%2C1%2C1%2C4%29%29 = %28matrix%282%2C1%2C-1%2C1%29%29, after left-multiplying both sides of the equation by A%5E%28-1%29 and simplifying.