modification of this uder pipeline.though you have clear your doubt freeof cost till final

Matrices
Let p is any point in the plane of two diormensional frame co-ordinate of the point p is (x_1,x_2)with respect to thex_1  x_2 and that of (y_1,y_2 ) with respect to the y_1  y_2 plane.

That is y_1  y_2is rotated angle θwith the previous plane x_1  x_2 therefore.
y_1=x,cos⁡θ+x_2 sin⁡θ
y_2=-x,sin⁡θ+x_2 cos⁡θ
These equation defined mapping of the x_1,x_2 plane into the y_1,y_2plane.
The general linear transformation is defined by the equation.
y_1=a_11 x_1+a_12 x_2+a…………………..+a_1n x_n
y_2=a_21 x_1+a_22 x_2+ …………………..+a_2n x_n
y_m=a_m1 x_1+a_m2 x_2+ …………………..+a_mn