write the following simultaneous equations in the form of AX= B where A,X and B are matrices
11x+6y=6
9x+5y=7
hence write the solution for x and y as a product of two matrices.
To write the given simultaneous equations in matrix form (AX = B), we need to arrange the coefficients of x and y in matrix A, the variables x and y in matrix X, and the constants on the right-hand side of the equations in matrix B.
The given equations are:
11x + 6y = 6 ...(Equation 1)
9x + 5y = 7 ...(Equation 2)
Now, let's form the matrices A, X, and B:
Matrix A:
A = | 11 6 |
| 9 5 |
Matrix X:
X = | x |
| y |
Matrix B:
B = | 6 |
| 7 |
Now that we have formed the matrices A, X, and B, we can write the simultaneous equations in matrix form as AX = B:
A * X = B
| 11 6 | * | x | = | 6 |
| 9 5 | | y | | 7 |
To find the solution for x and y, we can solve the matrix equation AX = B. We can find the solution (X) by multiplying the inverse of matrix A on both sides:
A^-1 * A * X = A^-1 * B
Since A^-1 * A gives the identity matrix, we have:
I * X = A^-1 * B
X = A^-1 * B
The solution (X) for x and y will be a product of two matrices:
X = | x | = A^-1 * B
| y |
To find the solution, you will need to calculate the inverse of matrix A, multiply it with matrix B, and obtain the matrix X with the values of x and y.