ENGR 328 Computational Methods in Engineering HW

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ENGR 328 Homework 5 Due: 02/21/2019 @ 2:00 pm Please upload a PDF of your homework including generated plots and any .m files you created. 1. A number of matrices are defined as: Answer the following questions regarding these matrices: (a) What are the dimensions of the matrices? (b) Identify the square matrices, column vectors, and row vectors. (c) What are the values of the elements: a12, b23, d32, e22, f12, g12? (d) Perform the following operations: 2. Given the equations: (a) Solve by Gauss elimination with partial pivoting. As part of the computation, use the diagonal elements to calculate the determinant. Show all steps of the computation. (b) Substitute your results into the original equations to check your answers. 3. Consider the tridiagonal system below: (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system’s condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a11 modified slightly to 0.52. Interpret your results. 4. A truss is loaded as shown below. Using the following set of equations, solve for the 10 unknowns, AB, BC, AD, BD, CD, DE, CE, Ax, Ay, and Ey. 5. Develop an M-file function to implement Gauss elimination with partial pivoting. Modify the function so that it computes and returns the determinant (with the correct sign), and detects whether the system is singular based on a near-zero determinant. For the latter, define “nearzero” as being when the absolute value of the determinant is below a tolerance. When this occurs, design the function so that an error message is displayed and the function terminates. The first line should look similar to: where D is the value of the determinant. Test your M-file for the following matrices using tol = 1 × 10-5. 1 [−1 −2 0 4 5 −9 𝑥1 −7 𝑥 −2 −1 3] 2 = 1 [ ] [ ] −1 −3 0 3 𝑥3 9 −3 −6 4 𝑥4 1 −1 1 𝑥1 2 [−6 1 −1] [𝑥2 ] = [3] 3 1 1 𝑥3 4

Tutor Answer

Super_Teach12
School: Duke University

Hi, here is your assignment :) Together with the m files :)

ENGR 328 Homework 5
1. A number of matrices are defined as:

%
%
%
%
%

Answer the following questions regarding these matrices:
(a) What are the dimensions of the matrices?
(b) Identify the square matrices, column vectors, and row vectors.
(c) What are the values of the elements: a12, b23, d32, e22, f12, g12?
(d) Perform the following operations:

A. Code:
(a) What are the dimensions of the matrices?
A = [4 7; 1 2; 5 6]
[m,n] = size(A)
Output:

B. Code:
%B. Identify the square matrices, column vectors, and row
vectors.
%
Square matrix are those with equal number of rows and
columns
%
Below is code for checking square matrix A = [4 7; 1 2; 5 6]
[m,n] = size(A)
if m == n
disp('A is square matrix');
else
disp('A is not a square matrix');
end
B = [4 3 7; 1 2 7; 2 0 4]
[m,n] = size(B)
if m==n
disp('B is square matrix');
else
disp('B is not square matrix');
end
Output:

C. Code:
% c) What are the values of the elements: a12, b23, d32, e22,
f12, g12?
A = [4 7; 1 2; 5 6]
[m,n] = size(A)
A(1,2)
B=[4 3 7;1 2 7;2 0 4]
B(2,3)
D=[9 4 3 -6;2 -1 7 5]
D(3,2)
Output:

D. Code:

Output:
B=
4

3

7

1

2

7

2

0

4

9

4

3

-6

2

-1

7

5

1

5

8

7

2

3

4

0

6

C=
3
6
1
D=

E=

ans =
5

8 15

8

...

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Review

Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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