9-4 Determinants and Cramer’s Rule

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Presentation transcript:

9-4 Determinants and Cramer’s Rule

Solving Systems Solve the Following equation:

Cramer’s Rule Cramer’s Rule is a neat way to evaluate systems and if you put the work in now you’ll do fine. It can be used for any size (2 by 2, 3 by 3 or even larger) system. It is easy to memorize and fast.

Definitions Determinant – a square array 2nd Order Determinant – a 2 by 2 array 3rd Order Determinant – a 3 by 3 array Elements – The things in the array

What does a determinant look like? A 2nd order determinant looks like this And the value of the determinant = Diagonal down right – diagonal up to right ae - bd

Examples Evaluate 1. 2. 9 – 1 = 8 2 – (-12) = 14

Why is this useful for systems? Lets work through an elimination example using all variables; then we can see how the determinant will be useful in solving. Just follow – you don’t need to write it down.

Lets eliminate y Look familiar?

If you apply the same process but eliminate x So, what does Cramer’s Rule say?

Cramer’s Rule Given a system Replace solutions in y column to solve for y Replace solutions in x column to solve for x Denominators are coefficient deterimanants

Group Problem Find the distance between: y=x-4 and the point (-2,4)