Matrices/linear transformations

Question 1

what does n and m represent (nxm)

Answer 1

n = rows
m = columns

Question 2

what does M^T mean

Answer 2

the transpose of the equation which means rows switch to columns

Question 3

How would you define a singular matrix

Answer 3

det = 0
det A = 0

Question 4

How would you reverse a 2x2

Answer 4

find det a and put 1/det a
switch a and d places
change signs of b and c

Question 5

How would you reverse 3x3

Answer 5

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

Question 6

What do you do with systems of equations

Answer 6

use simultaneous equations and solve

Question 7

how do you know if equations are consistent

Answer 7

when solving they all meet at one point and create a sheaf

Question 8

how do you know if they are inconsistent

Answer 8

they have no solutions and wont intersect at all

Question 9

what order of multiplication is BA

Answer 9

transformation a then b

Question 10

area of image =

Answer 10

area of object x modulus of det M

Question 11

What is an invariant point

Answer 11

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

Question 12

What is the only invariant point with a rotation of *

Answer 12

(0 ,0)