Using the simultaneous or matrix method to solve the following:
(1) 450alpha 4500B(beta).......eqn(2)
(2) 2000.7alpha 889511.22B...eqn(3)?
To use the matrix method, we can rewrite the given equations as a matrix equation in the form of AX = B.
First, let's represent the coefficients of the variables as a matrix A and the variables themselves as the column matrix X. Similarly, the constants on the right side of the equations can be represented as the column matrix B.
The given equations:
(1) 450alpha + 4500beta = ?
(2) 2000.7alpha + 889511.22beta = ?
We can write them in the matrix form AX = B as follows:
[ 450 4500 ] [ alpha ] [ ? ]
[ 2000.7 889511.22 ] [ beta ] = [ ? ]
The coefficient matrix A, variable matrix X, and constant matrix B are:
A = [ 450 4500 ]
[ 2000.7 889511.22 ]
X = [ alpha ]
[ beta ]
B = [ ? ]
[ ? ]
Now, to find the values of alpha and beta, we can solve the matrix equation AX = B using the inverse of matrix A.
First, calculate the inverse of matrix A:
A_inverse = inv(A)
Next, multiply the inverse of A with the constant matrix B:
X = A_inverse * B
Finally, calculate the values of alpha and beta from the variable matrix X.
Note: Since the values of B are not provided in the question, you need to complete the equation by replacing the question marks with the actual values in order to solve it.
Once you have the actual values of B, you can substitute them into the equation and use a matrix calculator or software to find the inverse of A and solve for X to get the values of alpha and beta.