matricies

Question 1

find inverse of 2x2 matrix

a b
( c d )

Answer 1

\_\_1\_\_  ( d  -b )
DET M ( -c  a  )

Question 2

find inverse of 3x3 matrix

Answer 2

calculate det(A)

replace each of the 9 elements with their minor (determinant of the 2x2 left when you remove the row and column of given element)

form Cofactor matrix ( change middle signs around edges, positive in corners and middle)

transpose (swap rows and columns)

1/det(A) x transposed matrix

Question 3

determinant of:

a b
( c d )

Answer 3

ad - bc

Question 4

singular

Answer 4

matrix can be reduced to a single point therefore has no inverse

Question 5

invariant line

Answer 5

a line which is not changed by a transformation

Question 6

line of invariant points

Answer 6

a line of points in which no points are changed by the transformation

Question 7

( x ) _____> ( ax + by )

y ) ______> ( cx + dy

Answer 7

transformation of (x , y) by:

a b
( c d )

Question 8

reflection in y = x

Answer 8

( 0 1 )

1 0

Question 9

reflection in y = -x

Answer 9

( 0 -1 )

-1 0

Question 10

reflection in x axis

Answer 10

( 1 0 )

0 -1

Question 11

reflection in y axis

Answer 11

( -1 0 )

0 1

Question 12

how to do matrix rotation

Answer 12

draw before and after, use formula book

Question 13

matrix representation of an enlargement

Answer 13

( a 0 )

0 b

Question 14

what do a and b mean in enlargement

a 0
( 0 b )

Answer 14

stretch factor a parallel to x axis
stretch factor b parallel to y axis
if a = b, simple enlargement with scale factor a

Question 15

area of transformed image = …

Answer 15

area of original x determinant

Question 16

what is the determinant

Answer 16

area scale factor

Question 17

how to find invariant point

From given transformation M

Answer 17

M( x ) = ( x )

_-( y ) = ( y )

Question 18

how to find invariant line

Answer 18

M__( x ) = ( x’ )

-___( mx + c ) = ( mx’ + c)