Forgottoen Flashcards
Rortsiron mateix
Cos , -sin
Sin. Cos
Leading diagonal the same, others same but diff sign
Shears
One acis fixed m shear happens parallel to thst direction
1 k
0 1 = shear parallel to x with x CONSTSNT and x y becoming k y
3d Transformation
Again look at identity matrix and loins on each axis and see what happens to thrm
Invariance 3 scenarios
Invariant point is any point thst is maoped on to itself by the transformation
The ORIGIN IS ALWAYS AN INVARIANT POINT
invariant line of points is a line where all points mapped on to themselves
Invariant line is just any point is mapped on to somewhere on that line
How to find all invwriant line of points and invsirnt lines
Line of points, x y , solve, if consistent yes
Lines
Put in x
Mx + c in
Put back into equation y = mx +c
Being ti right
Bare fsctorise to find values for m
See what happens when m is thid cancels out, then csn c take any vs,use, if m is this, c must be 0
What is determinant
Represents the scalar multiplier of the trsnfofmstuon
If area before was 2 , det is 5, now 10
As it’s a scalar mutltioel, applying two transformations together, the muktpileirs multipy,, so det AB is det A x det br
What does a NEGATIVE DETERMINANT DO TO A SHAPE
CHANGE THE ORIENTATION OF THE POINTS FROM CLOCKWISE TO ANTI
Negatife det just means orientation changed
What if det m is 0, what does this become, where do all points lie and now find equation
Det m 9 becomes SINGULAR MATRIX
Area is 0, all pointd on straight line now
Equation of new shape is by applying to x y and comparing y / x now (find scale fsctor)
This will always be c/a when det m is 0
If det is 0 does the inverse matricy exist snd why
No, because 1/ 0 but also thing about now ins trisgth line no way to find relationships ship back, lost info, no inverde
What Su inverse by normal
Identity m
