How do I solve these equations with a matrix to get $x$, $y$, and $z$? I'm unsure of how to start.
$0.09x + 0.10y + 0.12z = 52,000 \\ x + y + z = 500,000 \\ y = 2.5x$
How do I solve these equations with a matrix to get $x$, $y$, and $z$? I'm unsure of how to start.
$0.09x + 0.10y + 0.12z = 52,000 \\ x + y + z = 500,000 \\ y = 2.5x$
First, get rid of the decimals by multiplying the first and third equations by 100.
Next, write the three rows of the matrix A as:
A = {{9, 10, 12}, {1, 1, 1}, {-250, 100, 0}}
Next, write the column matrix for the solution:
b = {5200000, 500000, 0}
Solve by multiplying the inverse of A.b
A^(-1).b = {100000, 250000, 150000}
Verify the answer for each equation and it checks.
HTH