Matricies Flashcards
How to define matrices m x n what mean
Row then coloumn
What does confrokable mean when does it occur
It means for two matrices that are able to acc multiply with each other = conformabikity
Only happens when coloumns = rows
To apply a matrix as a trandofmsjton must?
Apply it INFRONTZ
How can represent a shape as a matrix?
As coordinates write them down and make sure to keep order the same
What is associate it’s and commuti it’s
Associate its is if (x+y) + z = x + (y+z)
Commutivity is x y = yx
What are the rules for matrix operations for associtivity snd commutivity and how to PROVE?
Prove using different letters and show they arentthe same
Addition multiplication is associative , subtraction isn’t
Addition commutivity, multiplication and subtraction arent
Remember commutivity rules don’t apply with which matrix
The identity
Sqaure , symmetric matrixes?
Sqaure ones are just same number of rows then columns
Symmetric is that there is line of symmetry in first diagonal top left to bottom right
Why would you use zero matrix
Using it ina edition and subtraction gives same result, it’s like the identity matrix for addition subtraction
Matrix Mut,illictual distributive?
Yes
This when you have P (X + y) and it becomes PX + PY this is what you’re tryna prove
Use letters again
Is reflection y=-x the same as rotation by 180?
NO, the points are at different oalced
Make sure that when finding matrix transformation ti multiply by
Make sure no more scalar multiples when start
Fir a rotation matrix, how to identify it?
And how to solve what the angle is?
Identify = leading diagonal must be the same and same sign
Other disganol must be the same and DIFFERENT SIGN = rotation matrix by some angle around the origin
Now if you have a clockwise rotwtion, then just subtrsvt from 360
To solve, equate it to cos theta and sin theta and find a solution which is consistent FOR BOTH
How to do rotation by any angle for 3d matrix? About an axis
Look at the axis and cancel it , any where on the field where that axis appears it becomes 0, and fill in rest with normal 2 by 2
Easy ti derrive, draw the axis nkw that are relevant and see what happens
