8. The weight of a vehicle is supported by reaction forces at its front and rear wheels as shown in the figure below. If the weight of the vehicle is 2400kg, the reaction forces R1 and R2 satisfy the following system of equations (equilibrium of forces and moments): R1 + R2 = 2400 6R1 = 4R2. W R1 R2 (a) Write the system of equations above in the matrix form AR = b, where R = RI R 2 (b) Find R1 and R2 by using Gaussian elimination on the augmented matrix. (c) Find R1 and R2 using the matrix inverse A-1.6. Find the indicated inverse matrix using Gaussian elimination on the augmented matrix. 1 1 3 1 1/3 13/3 7/3 C" ifC = 0 3 2 . Your result should be C" = 4/3 5/3 2/3 2 4 l 2 2 l 7. Use the inverse matrix of the previous exercise to solve the following linear system. x+y+3z=2 3y+2z=l 2x+4yz=3 . Find the matrix M that perform the following space transformations. Based on the determinant IM I mention whether the transformation shrinks or expands areas, and whether it inverts them. (5) H (i) (3') H (1) . Find the indicated determinant. 1 1 3 det(C)ifC= 0 3 2 2 4 1 . For the following system, state whether it is overdetermined, underdetermined or if there is a unique solution. 2x3y+Zz+r=l 4x+2y3zr=2 x+ y+ z+r=l . For the following system, use the matrix determinant to determine if there is a unique solution. (If there is, you do not need to calculate it.) x+ y+3z=2 3y+2z=l 2x+4y 3:0 . Write the following system of equations in matrix form, then form the augmented matrix [Alb], and solve these linear systems using Gaussian elimination on the augmented matrix. x+ y+3z=l 3y+2z=2 2x+4y z 2