Further maths

Things Ayush struggles to remember

About origin

Transfomration happens first by matrix A and then by matrix B
What is the transformation matrix?

BA

Finding invariant points and finding line of invariant points x y method

finding invariant lines, through the origin

TO find the area of matrix after transformation

The determinant of transformation matrix is the multiplying factor
So if matrix A has determinant 6
And the matrix A is applied to a triangle
the final image will be 6 times larger than original

Non singular matrix

determinant is non zero and inverse of matrix exists.

f(costheta) ———-90* anticlockwise————————f(sintheta)

cos(theata) curves are symmetrical about theta =0
sin(theata) curves are symmetrical about theta =pie/2

Where alpha is the angle between normal and line
Angle between normal and line + angle between plane and line =90*

Proof by induction divisibility

f(k+1)-f(k)

Proof by induction matrix

A^K+ 1 = A^k x A

Write this in summation form

The top part is not literally the last term shown in the series