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EE 5351 UMD SPRING, 2014 1. For the following system of equations, calculate by hand, showing your work: a. The A matrix for Ax=B form b. The B matrix c. Form the augmented 4x5 A|B matrix, and use Gaussian operations to produce the RREF of the augmented matrix. d. Use MATLAB (or other software) to check part c. 2w + x =1; 2x + y =1; 2y + z = 1; z=1 2. For the following matrices, calculate by hand: a. Rank(A), Trace(A) b. Det(A) c. Eigenvalues(A) d. Eigenvectors of A e. Check a-d with MATLAB (or other software) A = [-10 -7 ; 14 11] B = [2 16 8 ; 4 14 8 ; -8 -32 -18] C = [3 -2 5 ; 0 1 4 ; 0 -1 5] 3. A robotic arm moves in a 2D plane as shown below: Link A is 8 cm long and has a Joint, a, with 160 degrees of freedom at its base. A second link, B, is 6 cm long and is attached to the end of A using Joint b, with 90 degrees of freedom. An X-Y fixed frame of reference is established at the base of Link A. The end of the arm is labeled point, P. Find: a. Calculate the maximum length of the arm in the +X direction and give the P(x,y) coordinates of that point. b. Calculate the maximum length of the arm in the X direction when P(y)=0 (i.e. the end of the arm is touching the work surface) c. Find two sets of possible joint angles (a,b) when P (x,y) = (10,9) Scott Norr EE 5351 UMD SPRING, 2014 4. FOR GRAD CREDIT: For the robotic arm described above, write a MATLAB (or other software) script to calculate and plot the end position, P, for all possible joint values, in ½ degree increments. Scott Norr