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Besides the Hilbert matrix, there are other matrices that are inherently ill-conditioned. One such case is the Vandermonde matrix, which has the following form:
(a) Determine the condition number based on the row-sum norm for the case where
(b) Use MATLAB or Mathcad software to compute the spectral and Frobenius condition numbers.
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Chapter 10 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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- Suppose that three coordinate frames 0₁X1Y1Z1, 02X2V2Z2 and 03X3Y3Z3 are given, and 0]: P². p³ 1 0 R3 = 0 0.5 LO 0.866 Find p¹ and matrix R₂. E R F4 Q Search %6 5 F5 -0.866; R3 = 0 -1 0.5 T 我道 F6 F7 & 7 99- PrtScn FB Home F9arrow_forwardWhat is the determinant of a 1x 1 matrix? Show an example of this matrix.arrow_forwardThe differentials of point functions are exact differentials. Select one: O True Falsearrow_forward
- Suppose that the stiffness matrices of the above question (as shown below) are as follows: b -b a a K1 =108 x K2 =108 x -b -a a b 0.1 m 0.05 m 0.5 m 0.5 m where a= 1.8 N/m and b=2.9 N/m. Find the assembled stiffness matrix of the system using the following connectivity table. Element Node i Node j (1) 2 (2) 2 What is the summation of all terms located on the main diagonal of the assembled [a bc] stiffness matrix? (Hint: if the assembled stiffness matrix is b de then you e f need to find the value of a + d+ f). Your Answer: Answer The shape function value ) is zero at the centre of the element. O is always higher than 1. O is equal 1 at its own node and zero at other nodes. O is always less than 1.arrow_forwardThe shape function value O is always higher than 1. O is equal 1 at its own node and zero at other nodes. O is always less than 1. O is zero at the centre of the element.arrow_forwardQuestion 2: The 3x3 matrices A and B are defined in term of a constant k by: [1 -3 [k A = 15 9. 27 1 0. and B = -1 -1 11 [4 1 1 a) Find an expression for det A, in terms of k. e N b) Find the possible values of k given that AB is singular.arrow_forward
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