Question

How do you write a system of equations as a matrix equation?

Answer 1

Write the equations in standard form. Arrange the variables in the same order in each equation. Use the coefficients to fill the coefficient matrix. Put the variables in a vector that is multiplied by the matrix. Put the constants in another vector equated to the product of the coefficients and variables.

Example:
x - 2y = 3
-4x + 5y = -7
can be written in matrix form as

`\left[\begin{array}{cc}1&-2\\-4&5\end{array}\right]\cdot\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}3\\-7\end{array}\right]`