Solve the system using the inverse of a 2 × 2 matrix.

Question

Solve the system using the inverse of a 2 × 2 matrix.
3x − 2y = 3
−x + 5y = −1

Answer 1

Let the matrix A have the rows:

 

3 -2

-1 5

 

A^-1 = (1/det A)(cof A)^t

 

det A = (3)(5) - (-1)(-2) = 15 - 2 = 13

 

cof A = 

 

5        -(-1)

-(-2)   3

 

=

 

5   1

2   3

 

(cof A)^t = 

 

5  2

1  3

 

A^-1 = 

 

5/13  2/13

 

1/13  3/13

 

Then

 

x = (5/13)(3) + (2/13)(-1) = (15 - 2)/13 = 1

y = (1/13)(3) + (3/13)(-1) = (3 - 3)/13 = 0

 

Test the solution.