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Determine the condition number for the following system using the row-sum norm. Do not normalize the system.
How many digits of precision will be lost due to ill-conditioning?
(b) Repeat (a), but scale the matrix by making the maximum element in each row equal to one.
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Chapter 10 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- Find the determinant of the matrix using the formulas in number 1 then check your answer with shortcut solution in number 2. Please write the answer where I can clearly read the letters and numbers. Thank you. (Sometimes your x doesn’t read as x)arrow_forward3. Use the second method of frame assignment, and find the Jacobian of the following robot using the velocity propagation method (Ignore all theta related offsets): 03 02 L2 01 Please answer the question precisely and completely to use the second method of frame assignment to find the D-H table [alpha (i-1) , a (i-1) , d (i) , theta (i)], and find the jacobian matrix using the velocity propagation methodarrow_forward2. Consider the following matrix 10 0 140 A1 = 0 3 A2 = 1 1 1 , A3 = 1 0 -1 3 (a) Find the eigenvalues and eigenvectors of each matrix in (2). 1 10 010 1 2 3 (2) (b) Find the modal matrix M and diagonal each matrix (2) through similarity transforma- tion. Which matrix in (2) will lead to the Jordan form?arrow_forward
- subject linear algebra its linear algebris questionarrow_forwardA) Prove that the tool Jacobian matrix of the 3R Planar robot (shown in the figure) is given by the matrix below: -LS-LS-LS123 - L₁₂S12-L3 123-35123] V(a)=49+L2 + L3G23 1 L₂G12 + L3G123 1 B) Find the singular configuration of the robot. ჩვ. L3C123 1 02 L2arrow_forwardConsider the manipulator provided in the figure. Given the Position vector P w.r.t. to the base frame, derive the Analytical Jacobian for the position. Write your answer as J = [dpx/dq1 dpx/dq2 dpx/dq3; dpy/dq1 dpy/dq2 dpy/dq3; dpz/dq1 dpz/dq2 dpz/dq3] %3D Z3, Z4 Z1, Y, b,s, +b;C;82 -b,c +b3S152 -b;C2 X4 YA #3 b2 b3 O2, 02 P = #2 Z, Y3 #0arrow_forward
- The values of p and h which renders (makes) the following set of equations dynamically and statically decoupled are, respectively. k,+k2 5 p+4 x1 = 0, X2 7 h+1 + [7h+1 J+e 5 p+4 J+e h= -0.214 and p = -1.76 h = -0.143 and p= -0.8 h = -0.281 and p= -1.2 h = -0.081 and p = -0.536arrow_forwardPleasearrow_forwardTwo cables AB and AC are acting on the pole with forces FAB = 540N and FAC = 560N with parameters defining the attachment points shown in the table. We want to write the vector FAB in cartesian vector form. C X Y₂ parameters value units FAB 540 FAC 560 L ZI 3 7₂ 5.5 4 3.5 4 4 Submit Question N N m m m m m FAC A Y₁ Z write the vector FAB in Cartensian Vector Notation. Round your final answers to 3 significant figures. FAB= AB B L X1 Narrow_forward
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning