Solve Using an Inverse Matrix x-y=7 , x-y=5

Problem

{[x−y=7],[x−y=5])

Solution

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

A=[[1,−1],[1,−1]]

X=[[x],[y]]

B=[[7],[5]]

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

det(A)=(1)*(−1)−(−1)*(1)

det(A)=−1+1

det(A)=0

3. Determine if an inverse matrix exists. Since the determinant is 0 the matrix A is singular and does not have an inverse.

det(A)=0⇒A(−1)* does not exist

4. Analyze the system for solutions. Because the determinant is zero, the lines are either parallel or coincident. Comparing the equations x−y=7 and x−y=5 we see they represent parallel lines with different intercepts.

7≠5

Final Answer

No solution

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