Solve Using an Inverse Matrix (2x+4y)=6 , (4x+8y)=0

Problem

{[2*x+4*y=6],[4*x+8*y=0])

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=[[2,4],[4,8]]

X=[[x],[y]]

B=[[6],[0]]

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

det(A)=(2)*(8)−(4)*(4)

det(A)=16−16

det(A)=0

3. Determine the existence of an inverse matrix. Since the determinant is 0 the matrix A is singular (non-invertible).

det(A)=0⇒A(−1)* does not exist

4. Analyze the consistency of the system. Since the inverse matrix does not exist, the system is either inconsistent (no solution) or dependent (infinitely many solutions).

2/4=4/8≠6/0

5. Conclude that because the ratios of the coefficients are equal but do not equal the ratio of the constants, the lines are parallel and never intersect.

Final Answer

No Solution

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