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.
i really need to know how to do this i have posted it over again and no one is able to help me...
To write the given simultaneous equations in the form of AX = B, where A, X, and B are matrices, we need to organize the coefficients of x and y into matrices.
Let's start by rewriting the equations:
11x + 6y = 6 ........ (Equation 1)
9x + 5y = 7 ........ (Equation 2)
Now, we can form a matrix A which contains the coefficients of x and y in the same order as in the equations:
A = | 11 6 |
| 9 5 |
Next, we need to form a matrix X which contains the variables x and y:
X = | x |
| y |
Finally, we form matrix B which contains the constants from the right side of the equations:
B = | 6 |
| 7 |
So, the equation AX = B becomes:
| 11 6 | | x | | 6 |
| 9 5 | | y | = | 7 |
Now, to find the solution for x and y as a product of two matrices, we can solve for X by multiplying both sides of the equation by the inverse of matrix A:
AX = B ----> X = A^(-1)B
To find the inverse of matrix A, calculate the determinant (ad - bc), swap the positions of the elements on the main diagonal, and multiply each element by 1/determinant.
det(A) = (11*5) - (9*6) = 55 - 54 = 1
So, the inverse of matrix A is:
A^(-1) = (1/det(A)) * | 5 -6 |
| -9 11 |
Now, we can find X by multiplying A^(-1) and B:
X = A^(-1)B
| x | = (1/1) * | 5 -6 | * | 6 |
| y | | -9 11 | | 7 |
Simplifying the multiplication, we get:
| x | = | 5 -6 | * | 6 | = | 11 |
| y | | -9 11 | | 7 | | -13 |
Therefore, the solution for x and y in matrix form is:
| x | = | 11 |
| y | | -13 |
And that is the product of two matrices representing the solution for x and y.