Question

please answer all the questions! really need the help!

>of 5 4. ZOOM Page The questions listed below are intended to be answered using MATLAB which is available t p eapps.ps.edu. MATLAB are available lastpage o tis project, You should work out the solutions to these questions before starting the online quiz. You may use your solutions when you take the online quiz 1. Find the augmented matrix [Ab when T30, T 0, T = 20° and T= 10. 2. Use MATLAB to find the reduced row echelon form of the augnented matrix from question 1 3. Using vour solution from question find the vale of x 4. Use MATLAB to find A-. 5. Use MATLAB to find x using the equation x = Ab. Note that this answer shoukd be -1 to use when solving for ' Uving the rdcd rer ebakos fousss to find to find xi using the equation 6, Let T 0. T = 0. T, = 0° and T - 0Use MATLAB find x A-b 7. Let T 20 T20. T = 20 and T equation x A-b. 20. Use MATLAB to find x using the Use MATLAB to find x using the 0°. T= 20° and T 0 ution y 4-h 40 and T 40°, Use MATLAB to find x using the 9. .T couation x A-b. 10. Let T40r, T = 40, T = 0° and T = 0. Use MATLAB to find x using the equation x A-'b MATLAB Instructions 1. Enter a matrix by entering the rows separated by a semi-colon 4 -1-1 0 -1 4 0-1 For example, to enter the matrix A = -1 0 4 -1 0 1-1 4 enter A 4-1-1 0 -1 40-1-104-l:0-1-1 4]. 2. Enter a vector by entering each number separated by a semi-colon | li+T, For example, to enter the vector b= T3+T T2+T [Ti Ti : Ti + T2 : T3T4: T2 + T3]. enter b Note that you will first need to enter Ti, T2, T3 and T1. To enter Ti all you need to do is to type Ti = the number it equals 3. Create an augmented matrix by entering each matrix separated by example, to enter [A]b], enter [A,b]. It is best to rename the augmented matrix. For example, name the augmented matrix [A,b] C by entering C=[A,b]. a comma. For 4. To find the reduced row echelon form of a matrix, C for example, enter rref(C) 5. To find the inverse of a matrix, A for example, enter inv(A) 6. To multiply a matrix times a vector, A-'b for example, enter inv(A)*b

Answer 1

Editor Q1.m Command Window Q1.m Untitled2 X + A input ('Enter matrix A: '); Tl input ('Enter Tl:'); 1 3 T2-input ('Enter T2: '); 4 T3=input ('Enter T3: '); - T4 input ('Enter T4:'); 5 - b [T1+T4 Tl+T2; T3+T4; T2+T3 ]; fprintf ('Answer 1: The augmented matrix is: '); CE[A, b fprintf ('Answer 2: The reduced row echelon form of augmented matrix is: ') 7 8 10 R=rref (C) fprintf 'Answer 3: The value of x is:'; X1-R (, end) 11 - 12 fprintf'Answer 4 The inverse of matrix A is: '); 13 Al-inv (A) 14 is: ) fprintf ('Answer 5: The value of x 15 - X2-inv (A) *b 16- -

Editor- Q1.m Command Window >>Q1 Enter matrix A: [4 -1-1 0; -1 40 -1; -1 0 4-1; 0 -1 -1 41 Enter Tl:30 Enter T2:0 Enter T3:20 Enter T4:10 Answer 1: The auqmented matrix is: C 4 -1 -1 40 -1 -1 30 4 0 -1 0 4 -1 30 0 -1 -1 4 20 Answer 2: The reduced row echelon form of augmented matrix is: R 1.0000 17.5000 0 0 15.0000 0 1.0000 0 0 1.0000 15.0000 1.0000 0 0 12.5000 Answer 3: The value of x is: X1 17.5000 15.0000 15.0000 C

Answer 4: The inverse of matrix A is: Al = 0.0833 0.0417 0.2917 0.0833 0.0833 0.2917 0.0417 0.0833 0.0833 0.0417 0.2917 0.0833 0.0417 0.0833 0.0833 0.2917 Answer 5 The value of x is: X2 17.5000 15.0000 15.0000 12.5000

te melho of uaing for Aohing duced ros echelon orm ol e augmenta matrix is easier thovn the mehod of aecausebon any inverae of A, using madrix A f order grater han 3, e inverse 04ily oP educed vow echelon onm of the augmnted oniginal tom f1uatis ruces comparatively nay aytem But in he can't be caleulated case matrix, e to olhe to The MATLAB acript for qeeskons 6-10 is givew ey

Command Window F Q1.m Q2.m A input ('Enter matrix A: '); 1 T1-input ('Enter Tl:'); 2 3 T2-input 'Enter T2: '); T3-input (' Enter T3: '); 4 T4-input ('Enter T4: '); 6 b [Tl+T4;Tl+T2 ; T3+T4 ; T2+T3 ] Al-inv (A); _10 fprintf ('Answer X inv (A) *b The value of x is:'); 9

Editor Q2. Command Window >> Q2 Enter matrix A: [4 -1 -1 0; -1 4 0 -1; -1 0 4-1; 0 -1 -1 41 Enter Tl:0 Enter T2:0 Enter T3:0 Enter T4:0 Answer 6: The value of x is X o ooO

>>Q2 Enter matrix A: [4 - -1 0; -1 40-1:-1 o 4-1; 0 -1 -1 41 Enter T1:20 Enter T2:20 Enter T3:20 Enter T4:20 ble ble Answer 7: The value of x is: 0:40] X = 20.0000 20.0000 20.0000 20.0000;20 20.0000

Command Window Ec >> Q2 Enter matrix A: [4 -1 -1 0;--1 4 0-1; -1 0 4-1; 0-1-1 41 Enter Tl:20 Enter T2:0 Enter T3:20 Enter T4:0 Answer 8: The value of x is: X= 10.0000 10.0000 10.0000 10.0000

>>Q2 Enter matrix A: [4 -1 -1 0; -1 4 0-1; -1 0 4-1; 0 -1-1 41 Enter Tl:0 Enter T2:0 Enter T3:40 Enter T4:40 Answer 9 The value of x is: X= 20.0000 10.0000 30.0000 20.0000 0000:30

>> Q2 Enter matrix A: [4 -l -l 0;-1 4 0-1; -l 0 4-1: 0 -1 -1 41 Enter Tl:40 Enter T2:40 Enter T3:0 Enter T4:0 Answer 10: The value of x is: X= 20.0000 30.0000 10.0000 20.0000 o.10
In the MATLAB script for question 6-10 , I have just change the line 8, in fprintf the question number is changed for each case.