The question is in the picture below 1Consider theellipse pictured below, with semimajor axis of length 3 and at a 30 degree angle withthe x-axis, and with and semiminor axis with length 2.30°(a) Find a matrix A, that representsthis ellipse. Hint: You may want to think of your transformation as a compositionof rotations and scaling.transformation that takes the unit circle to(b) Use the determinant to compute the area of the ellipse.(c) If R is a region of the plane with area equal to 7 units?, what is the area ofthe image of this region after it undergoes the transformation represented by thematrix 2A?2

Scaling matrix S, if a times scaling in x direction and b times scaling in y-direction. S = a00bRotation matrix R, with θ angle rotation from +ve x-axis in anti-clockwise direction. R = cosθ-sinθsinθcosθ Equation of unit circle centered at (0,0)x2 + y2 =1Rotation of of circle,C by θ =30°C' = RCx'y' = cos30°-sin30°sin30°cos30°xyx'y' = 32-121232xyx'y' =32x -12y12x +32yScaling of circle C' to ellipse,E with a= 3 and b = 2 E = SC'x''y'' = 3002x'y'x''y'' = 300232-121232xyx''y'' =332-3213xyx''y'' =AxyWhere A =332-3213 Area of ellipse= detA * area of circledetA =det332-3213detA = 92+32 = 6area of cirlce = π*12 = πAr(E) =6*πArea of ellipse = 6π unit2area of region R = 7 unit2Transformation using 2A. detrminant of 2A = 2*detA = 2*6detrminant of 2A =12area of R after transformation using 2A = det(2A) * area of region R = 12*7area of R after transformation using 2A = 84 unit2