Solve Using an Inverse Matrix 2x-y=9 , 6x-3y=9

Problem

{[2*x−y=9],[6*x−3*y=9])

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,−1],[6,−3]]

X=[[x],[y]]

B=[[9],[9]]

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

det(A)=(2)*(−3)−(−1)*(6)

det(A)=−6−(−6)

det(A)=0

3. Determine the existence of the inverse matrix A(−1) 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 consistency of the system. Since the rows of the augmented matrix are multiples but the constants are not in the same ratio, the lines are parallel.

2/6=(−1)/(−3)≠9/9

Final Answer

No solution

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