Matrices/linear transformations Flashcards
what does n and m represent (nxm)
n = rows
m = columns
what does M^T mean
the transpose of the equation which means rows switch to columns
How would you define a singular matrix
det = 0
det A = 0
How would you reverse a 2x2
find det a and put 1/det a
switch a and d places
change signs of b and c
How would you reverse 3x3
find det a and put 1/det a
make a matrix of minors using each sets of 2x2
form a matrix of cofactors
transpose the matrix
can check with all numerical values on a calculator
What do you do with systems of equations
use simultaneous equations and solve
how do you know if equations are consistent
when solving they all meet at one point and create a sheaf
how do you know if they are inconsistent
they have no solutions and wont intersect at all
what order of multiplication is BA
transformation a then b
area of image =
area of object x modulus of det M
What is an invariant point
one which isnt chnaged by a transformation
or each point on the line is transformed to the same point on the line
eg y=x
What is the only invariant point with a rotation of *
(0 ,0)
