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 the form of AX = B, where A, X, and B are matrices, we first need to identify the coefficients of the variables x and y and arrange them in matrix form.
The given equations are:
11x + 6y = 6 -------- (Equation 1)
9x + 5y = 7 -------- (Equation 2)
Now, let's identify the coefficient matrix, X matrix, and B matrix.
Coefficient matrix (A):
The coefficient matrix contains the coefficients of the variables x and y. In this case, it will be a 2x2 matrix.
A = {{11, 6}, {9, 5}}
X matrix:
The X matrix contains the variables x and y. It will be a 2x1 matrix.
X = {{x}, {y}}
B matrix:
The B matrix contains the constant terms on the right side of the equations. It will be a 2x1 matrix.
B = {{6}, {7}}
Now, we have A, X, and B matrices in the equation AX = B.
Writing the given equations in matrix form:
A * X = B
{{11, 6}, {9, 5}} * {{x}, {y}} = {{6}, {7}}
To find the solution for x and y as a product of two matrices, we need to find the inverse of matrix A first.
A^-1 is the inverse of matrix A.
A * A^-1 = I, where I is the identity matrix.
After finding the inverse of A, the solution for X can be determined as follows:
X = A^-1 * B
Finally, the solution for x and y as a product of two matrices would be:
{{x}, {y}} = A^-1 * B
Note: The actual calculation of A^-1 and X requires numerical computations, which are not part of this explanation.