Solve Using an Inverse Matrix 2x-5y=4 , 3x-2y=-5

Problem

{[2*x−5*y=4],[3*x−2*y=−5])

Solution

1. Write the system in matrix form A*X=B where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

A=[[2,−5],[3,−2]]

X=[[x],[y]]

B=[[4],[−5]]

2. Calculate the determinant of matrix A denoted as |A| or det(A) using the formula a*d−b*c

det(A)=(2)*(−2)−(−5)*(3)

det(A)=−4+15=11

3. Find the inverse matrix A(−1) using the formula A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/11*[[−2,5],[−3,2]]

4. Solve for X by multiplying the inverse matrix A(−1) by the constant matrix B such that X=A(−1)*B

X=1/11*[[−2,5],[−3,2]]*[[4],[−5]]

5. Perform matrix multiplication to find the values of x and y

X=1/11*[[(−2)*(4)+(5)*(−5)],[(−3)*(4)+(2)*(−5)]]

X=1/11*[[−8−25],[−12−10]]

X=1/11*[[−33],[−22]]

X=[[−3],[−2]]

Final Answer

[[x],[y]]=[[−3],[−2]]

Want more problems? Check here!