Matrix Flashcards
Inverse of a 2 x 2 matrix?
[ a b ] = 1/ det A [ d -b ]
[ c d ] = [ -c a ]
How to know if there is an inverse to a matrix?
- Using Determinant of a Matrix
- If det A = 0 (inverse does not exist)
-If det A is not 0 (inverse does exist)
What if a matrix is SINGULAR?
det a = 0
What if Matrix is NOT SINGULAR
det a does not equal 0
How to work out det A
(A x D) - (B x C)
How to double check an inverse of a matrix?
AA^-1 = I
What are invariant lines?
Points which are mapped onto themselves
What are some invariant lines?
-Mirror line
- Lines perpendicular to mirror line
Invariant points?
Points in mirror line, which do not change
When are there no invariant lines?
-In a rotation, theta does not equal 180 degrees
When are there invariant lines in a rotation?
-When theta is equal to 180 degrees
-any line that passes through origin is invariant
Matrix for reflection in y axis? (x=0) (DO)
( -1 0 )
( 0 1 )
Matrix for reflection in x axis? (DO)
( 1 0 )
( 0 -1 )
Matrix for reflection in x axis? (y=0) (DO)
( 1 0 )
( 0 -1 )
Reflection in y=x (DO)
( 0 1 )
( 1 0 )
Reflection in y=-x (DO)
( 0 -1 )
( -1 0 )
How do you find the line invariant points of a matrix?
Matrix x (x) = (x)
(y) (y)
How do you find invariant lines of a matrix?
Matrix x (x) = (x) then sub that into y = mx+c
(mx+c) (y)
TIP = for final answer always factor out x and c
If you have a reflection that is y= x + 1 for etc? (DO)
Use translation for ( 1 0 0 )
( 0 1 -1 )
( 0 0 1 )
Reflection for 3D? (DO)
x y z
( 1 0 0 ) make it -1 for what plane the question asks for
( 0 1 0 )
( 0 0 1 )
