Matrices

Page 1

Further Pure; Chapter n;

Matrices: -

[10] - Identity Matrix

[01]

[cos(pheta) -sin(pheta)] ---> Anticlockwise Rotation through pheta about O

[sin(pheta) cos(pheta)]

[cos(2pheta) sin(2pheta)] -----> Reflection in the line y = (tan(pheta))x

[sin(2pheta) -cos(2pheta)]

M = [ 2 -1] ==> 3M = 3[2 -1] ==> 3M = [6 -3]

[4 5] [4 5] [12 15]

[a , b] x [p , q] == [ap + br , aq + bs]

[c , d] x [r , s] == [cp + dr , cq + ds]

[a , b] x [p] == [ap + bq]

[c , d] x [q] == [cp + dq]

Transformations;

M [1] ==> [a , b] [1] ==> [a]

[0] ==> [c , d] [0] ==> [c]

M [0] ==> [a , b] [0] ==> [b]

[1] ==> [c , d] [1] ==> [d]

Two transformations

M1M[x]

[y]

MM1 =/ M1M

[a , b] ==> Reflection & an Enlargement

[b , -a]