Mastering Linear Algebra: Using Elementary Row Operations To Manipulate Matrices And Solve Systems Of Equations.

Elementary row ops permit one equation in a linear system to be subtracted from another.

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Elementary row operations are used in linear algebra to manipulate a matrix in order to solve a system of linear equations. One of the elementary row operations is subtracting one row from another row. When performing this operation, we subtract the entire row of one equation from the corresponding row of another equation.

For example, let’s consider the system of equations:

“`
2x + 3y – z = 7
x – 2y + 4z = -1
3x + y – 2z = 8
“`

If we want to eliminate the `x` variable from the second and third equations, we can use the first equation to subtract the `2x` term from the second equation and the `3x` term from the third equation. This will give us a new system of equations:

“`
2x + 3y – z = 7
-8y + 6z = -15
-5y + 5z = -13
“`

We can see that we have eliminated the `x` variable from the second and third equations using the first equation. This is possible because of the properties of systems of linear equations and the way the equations are written in a matrix form.

Therefore, subtracting one equation from another is one of the elementary row operations that allows us to manipulate a system of linear equations in order to solve it.

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