Determinants Flashcards
What does the determinant 2x2 mean and 3x3
2x2 is the AREA MULTIPLIER, 3x3 is the volume scale multipler!
What happens if the DET is negative!
This REVERSES THE ORIENTATION OF THE SHAPE, so if it was going clockwise, after the transformation, it will be ANTI CLOCKWISE
How to find 3 x 3 detemrinant
Rememebr +-+ matrix,
Pick row with most 0
And then take that number, times by +- matrix, then vover row and column snd find det if remaining 2x2
If det = 0 then what it means
What do they plot on to
How to find equation
A singular matrix, that has no 0
Naturally new area is 0, and thus is plotted on a STRAIGHT LINE
To find equation of line, apply matrix to general x y, and see how y compared to x to find the equation!
If matrices are inverse if one another, what do they multiply to give and whatnhappens transformation wise
They multiply to give I the identity matrix, and the inverse matrix REVERSES THE Transformation of original
How can you sue inverse matrix to solve problems
Apply inverse to A to get rid of it, and apply inverse on right hand sife to as itd equation.
This should give you the coordinates of xy
Why does det m = 0 have no inverse
It maps on a line, and so no way ti get back from this line, info is lost forever, no inverse, = singular
This makes it NON UNIQUE?
Why ar einverse matricied UNIQUE?
As the inverse and normal are COMMUATIVE, it means it is UNIQUE
HOW TO PROVE THE INVERSE OF AB IS B-1A-1?
Why this make sense anyways?
Let inverse of AB =X
So that X AB = I
Now POST MUKTIPLY B-1 to bith, remove B
Post multiply A -1 to both, remove A
And you get X = B-1A-1
2) makes sense bevause if you do B then A, need tk remove A so A-1, then remove B, so B-1A-1!
How to find inverse 3x 3 don’t be stupid
First find det
Now find matrix of cofactors, this is where you do det for each number, but make it multiplied by +- + matrix
Then transpose it, so make row column
Now multiply by 1/det
