Solve Using an Inverse Matrix x+3y=10 , 3x+9y=16

Problem

{[x+3*y=10],[3*x+9*y=16])

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=[[1,3],[3,9]]

X=[[x],[y]]

B=[[10],[16]]

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

det(A)=(1)*(9)−(3)*(3)

det(A)=9−9

det(A)=0

3. Determine the existence of an inverse by checking if the determinant is non-zero.

det(A)=0

4. Conclude the solvability of the system using the inverse matrix method. Since the determinant is zero, the matrix A is singular and does not have an inverse. This means the system either has no solution or infinitely many solutions.

5. Check for consistency by comparing the equations. The second equation 3*x+9*y=16 is equivalent to 3(x + 3y) = 16,w*h*i*c*h*i*m*p*l*i*e*s() + 3y = \frac{16}{3}.T*h*i*s(c)*o*n*t*r*a*d(i)*c*t*s(t)*h*e*ƒ*i*r*s(t)*e*q*u*a*t*i*o*n + 3y = 10$.

Final Answer

No solution

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