I'm having difficulties to solve these problems.

x - 2x. +4x. =1 2. Consider the following system of equations x - 2x, - 3 x x -2 (a) Write the system as a matrix equation: Ax - b (b) Solve the matrix equation using inverse matrices (you may use your calculator) or explain why this won't work. If the inverse method fails, please solve the system by methods of Chapter 1. 3. In 2D video games, many movements are modeled by matrices applied to an object through matrix multiplication. Consider an object in the first quadrant with its position described by the vectory - (x. y) . Please use the Geogebra: Effect of Matrix Multiplication applet in the Canvas Project Modules to help you answer the following questions. You may also want to consider using the 2-D rotation matrix R.= coso - sind sin & cose (a) Find a matrix of such that when applied to any vector v = ( x. y)' as in Av will cause the object to be rotated 45" counterclockwise. (b) Now, find a matrix F such that when applied to the vector v = (x, ") as in Fv will cause the object to be "flipped" about the y-axis (e) Now, find a matrix A' that will take the transformed vector in part (a) back to its original position using matrix multiplication as in '( by)- (d) Now, find a matrix F' that will take the transformed vector in part (b) back to its original position using matrix multiplication as in F( Fy) - v. (e) What happens to your vectors if you apply both transformations in parts (a) and (b), such as A( Fv) or F ( Av)? Does the order matter here (le. do they accomplish the same action?)