Linear algebra

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Linear Function[edit | edit source]

For any 2 point A(0,0) , B() a straight line can be drawn . The slope of the line is

Therefore,

For a point C() on the same line of the slope m

Linear Equations[edit | edit source]

Has general form

with
with

System of Linear Equations[edit | edit source]

Example[edit | edit source]

Roots of system of equations[edit | edit source]

Variable Elimination[edit | edit source]

Multiply 1st row by 2 add to 2nd row

Yields

=>

Multiply 1st row by -3 add to 2nd row

Yields

=>

Substitution[edit | edit source]

If you get a system of equations that looks like this:

You can switch around some terms in the first to get this:

Then you can substitute that into the bottom one so that it looks like this:

Then, you can substitute 2 into an x from either equation and solve for y. It's usually easier to substitute it in the one that had the single y. In this case, after substituting 2 for x, you would find that y = 7.

Determinant[edit | edit source]

If you get a system of equations that looks like this:

Solve for y

Solve for x

Find Roots of System of Linear Equations systematically[edit | edit source]

Eliminate variable x

Add

Solve for y

Eliminate variable y

Add

Solve for x

Reference[edit | edit source]


External links[edit | edit source]