# MEC 320 SUNY at Stony Brook Engineering Design Numerical Methods Questions

User Generated

FnzCbegre41

Engineering

MEC 320

SUNY at Stony Brook

MEC

## Description

Hi! I have some questions that need to be answered VERY soon so I only need the answers for the multiple-choice.

Please put the question number and the correct choice next to each other, thank you!

### Unformatted Attachment Preview

Question 3 A linear programming problem with the two design variables X1 and x2 has the following constraint: x1+x253. This constraint can be reformulated as x1+x2+x3 = 3. Which of the following statements is generally true about X3, at least as discussed in this course? a. It automatically becomes a design able. b. It is a slack variable. C. It is a surplus variable. d. It is less than zero. O O e. It is not processed during the linear programming procedures. f. It does not appear in the tableau. g. None of the Above Question 6 If a 11 = 212 = Q 21 = Q 22 = 1, the sum of all the elements of the adjoint matrix is a a. O b. 1 c. 2 d d.-1 e. -2 f. 4 ОО g. None of the Above Question 7 Consider the data below XO X1 X3 X2 5 X 1 1 2 7 у 4 9 6 11 The first divided difference f[x2,X1] is a. 5/2 b.-1 c. 5 O d. 7/6 e. 1/2 f. 1/5 g. None of the Above Question 10 Consider the matrix whose elements are 911 = 4, 212 = 0, A21 = 0, 222 = 5. The largest eigenvalue of the matrix is probably a. 4 b.5 c. 20 d. 1 e. 10 f. 8 O g. None of the Above Question 11 The function f(x,y) = x2–2x+y is to be optimized subject to x-y=1. To do this, the augmented function F"(x,y,X)=x2-2x+y+(x-y-1) is used. What is the value of x for an optimized function? a. 1 b. 1/2 C. -1/2 O d.-1 e. O f. 2 g. None of the Above Question 12 The roots of the equation f(x)=x2-3x+ is to be found with the successive iteration method using the algorithm: =[-(xM)1/2+3xmy1/2 m+1 х If the initial guess is x = 1, what is x after the first iteration? a. 1.732 O b. 2 c. 1.414 O d. 1 e. -1.732 f. 1.732 i, i = -1 O g. None of the Above Question 13 Consider the following system of equations x1 + x2 = 4 4x1 +4x2 = 16. What can you say about the solutions of these equations? a. There are no solutions. b. There is an infinite number of solution. c. The solutions are unique. d. x1 = 0, X2 = 0 can be a solution. e. We have an ill-conditioned system. f. x1 +0,X2 + is a solution. g. None of the Above Question 17 Consider the data below x 1 2 3 y 2 8 7 3 What is Siv(x) dx using two applications of Trapezoidal Rule? a. 20.5 b. 8.5 c. 10.0 d. 12.5 e. 13.667 f. 25.0 g. None of the Above Question 18 Consider the following system of equations: x1 + x2 = 3 2x1 + 2x2 = 5. What can you say about the solutions of these equations? a. There are no solutions. b. There is an infinite number of solutions. c. The solutions are unique. O d. x1 = 0, x2 = 0 can be a solution. e. We have an ill-conditioned system. o . f. x1 *,X2+ is a solution. g. None of the Above Question 23 Given values of x = 1.0, y=1.0, with the errors AX =0.01, Ay=0.01, estimate the resulting error in the function f(x)= x²y. a. 0.03 b. 0.04 c. 0.01 d. 0.02 e. 0.005 f. O g. None of the Above Question 24 Consider the data below X 1 4 6 у 0 1 3 Using the Lagrange interpolation and the notations adopted in the course, what is f1(2)? a. 1/2 b.-2/3 c. 1/4 d. -1/2 e. 2/3 f. 1/3 ОО g. None of the Above Question 25 We want to fit a linear regression: y=20+21x to the following data X 1 2 00 W у 1 3 The sum of squares of the errors is a. 0.5 O b.-0.5 O c. 1.5 d. 1 e. -1 O o f. 2.5 g. None of the Above Question 28 If the determinant of matrix A is non-zero, which of the following statements is not true? a. The matrix is invertible. b. The matrix is non-singular. o c. The matrix has a full rank. d. No zero columns or rows can be found after a Gauss elimination procedure has been performed on the matrix. e. Considering the matrix as an operator, we can use the direct inverse method to solve for x in Ax = b. f. Considering the matrix as an operator, we can use Cramer's Rule to solve for x in Ax = b. g. None of the Above Question 29 We want to fit a linear regression y=ao+ax to the following data: X 1 3 5 y 3 5 The value of ay is a. 1/2 b.2.5 c. 1.0 d.-6/23 e. -2.5 f. 0 g. None of the Above Question 30 We want to fit a linear regression: y=ao+anx to the following data X 1 2 3 y 1 3 8 The error (that is, 73-00-24x3) of the fitted curve for the third point (x = 3, y=8) is approximately equal to a. -1 O b.-0.5 O c. 3.5 d.-3 o e. 0.5 Ο Ο Ο f. 1 g. None of the Above Question 32 We want to fit a linear regression y=20+ajx to the following data: X 1 3 5 у 3 4 5 The error for the first point (x = 1, y = 3) (or 71 -a, -21x1) is a. 1/2 O b.-1/2 O c. 2.5 d.0 e. -2.5 f. 1.0 O g. None of the Above
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

View attached explanation and answer. Let me know if you have any questions.PFA the solutions for the questions.

clack

aiahle
...

### Review

Anonymous
Nice! Really impressed with the quality.

Studypool
4.7
Indeed
4.5
Sitejabber
4.4