Suppose T: M2,2→→P2 is a linear transformation whose action on a basis for M2,2 is as follows: [1]- Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the character to indicate an exponent, e.g. ax^2-bx+c. = -2x+5 = 0 =-x+4 T -2-2 -4-2 = 2x²+4x-26 T 02 = -2x²+2x+10

2. Write down the matrix of the given linear transformation withrespect to the standard bases of the domain and codomain.

Write down the 2 × 2 matrices that represent the following linear transformations ofthe plane. Also draw the image of the (first quadrant) unit square 1 under each transformation.(a) A dilation with horizontal dilation factor 2 and vertical dilation factor 1/2.(b) A vertical shear with factor −1/2. (c) A rotation of 450 anticlockwise. (d) A reflection across the line at angle −300 to the X-axis. (e) The transformation T(x, y) = (2x + 6y, x + 3y).

Please explain every steps in detail