HW10: Problem 6 Previous Problem Problem List Next Problem (2 points) Let: -10 10 1 A = 15 -10 -11 14 5 Verify that this matrix corresponds to a rotation of RS: AA = det (A) = Find a vector parallel to the axis of rotation. Compute the trace of A. tr( A) = Compute the rotation angle of A, in degrees. (You shouldn't need a large amount of work to do this - see the hint below if you get stuck.)HW10: Problem 6 Previous Problem Problem List Next Problem Results for this submission Entered Answer Preview Result 10 0 010 010 correct 0 0 0 correct N w - incorrect -0.465657 correct 137.16 137.16 correct At least one of the answers above is NOT correct. (2 points) Let: 10 10 A = 15 -10 11 14 - 2 Verify that this matrix corresponds to a rotation of RS: A'A= det (A) = 1 Find a vector parallel to the axis of rotation. 3 2 Compute the trace of A. tr(A) = -7/15 Compute the rotation angle of A, in degrees. 137.16 (You shouldn't need a large amount of work to do this - see the hint below if you get stuck.) Hint:Steps as AAT = 1 and def ( A ) = $ 1 Now the mats corresponding to the eigen value AX = d x AX = (1 ) X where X = [ x y z ] The matrix - 10 10 2 IS -10 - 11 - 2 S 15 21 - 10 15 2 = ? - * 1 ) 2 n - IS - 11 TY Z = y 15 ( 2 ) 14 IS 2 - y is 2 = Z - ( 3 ) by Solving thesed equations 21 = - 0.846.2 J = - 1. 0326 2 then Jetting 2 =K (K belling a mom- zozo constant) * = 1-0.8461 , #- 10326 1, 1 ] X = 1X/- 0-846#, - 1:0326, 17tTherefooce, by definition it follow that the axis of rotation of A is the vectorix Henie a vectore y parallel to the axis of rotation 18 given by L Y = PX = P ( K [ = 0. 8 46 , - 1 . 0326 , 1 ) ' ] That's - 0:846 Y = RC - 1:0326 where PK it should be noted that P i's mom zero