Answer to Question #324456 in Linear Algebra for Cee

Question

3. The geometrical representation of a vector v =



a

b

is an arrow starting at the origin and ending at the point (a, b).

Multiplication of a vector v with the matrix A =



cos θ − sin θ

sin θ cos θ



yields a vector p =Av

which is a counter clockwise rotation of v by an angle of θ.

a) Find the vector p that is obtained if v =



3

−4



is rotated counter clockwise by 40â—¦

.

b) Find the vector q that is obtained if v =



2

3



is rotated clockwise by 40â—¦

.