For example, in the linear equation 2x + 4y = 8, x and y are variables. The constant is 8. The numbers 2 and 4 are coefficients.
The linear system above, for example, can be rewritten as a matrix equation as follows: A x X = C.
For example, consider the following linear system:2x + 4y = 8x + y = 2Your augmented matrix would be a 2x3 matrix that looks like this:
swapping two rows. multiplying a row by a number different from zero. multiplying one row and then adding to another row.
For example, say you have a matrix that looks like this:You can keep the first row and use it to produce zero in the second row. To do that, first multiply the second row by two, as follows:
In the example above, multiply the second row by -1, as follows:When you complete the multiplication, your new matrix looks like this:
In the example above, add the two rows together as follows:
For the example above, your new system would therefore look like this:
In the example above, you’ll want to “backsolve” – moving from the last equation to the first when solving for your unknowns. The second equation gives you an easy solution for y; since the x has been removed, you can see that y = 2.
In the example above, replace the y with a 2 in the first equation to solve for x as follows:
