Question

10 9:17 X ull ** - STC Report Lab - للقراءة فقط (1) 28 Hoď → 7 سجل دخولك لتحرير الملف وحفظ التغييرات ا... Problems Problem 1: The following polynomials are given: Py(x) = x + 2x4 - 3x + 7x2 - 8x + 7 Polx) = x + 3x - 5x2 + 9x + 11 P3(x) = x - 2x - 3x +9 P4(x)=x2-5x + 13 Ps(x) = x + 5 Use MATLAB functions with polynomial coefficient vectors to evaluate the expres- sions at x = 2 Problem 2: Consider the two matrices BE [ 3 21 i -15j 5; 10+ i] 2118 Using MATLAB, determine the following: (a) A+B (b) AB (C) A? (d) AT (e) B! BAT (g) A + B2 - AB Problem 3: Determine eigenvalues and eigenvector of A using MATLAB. (a) A-05-08) 6)-(3) 0.75 Problem 4: Determine the eigenvalues and eigenvectors of A and B using MATLAB 45 - 31 (a) A = -1 2 3 [257] 12 B = 8 96 5 3 - 1

solve these questions by Matlab

Answer 1

(1)

Command Window >> pl = [1 2 -3 7 -8 7]; >> polyval (p1,2) ans = 59 >> p2 = (1 3 -5 9 11]; >> polyval (p2,2) ans = 49 >> p3 = [1 -2 -3 9]; >> polyval (p3, 2) ans = >> p4 = [1 -5 13]; >> polyval (p4,2) ans = >> p5 = [1 5]; >> polyval (p5,2) ans = - fr >|

(2)

>> A = [3 2*pi; 5*j 10+sqrt(2)*j];
>> B = [7*j -15*j; 2*pi 18];
>> A+B

ans =

3.0000 + 7.0000i 6.2832 -15.0000i
6.2832 + 5.0000i 28.0000 + 1.4142i

>> A*B

ans =

1.0e+02 *

0.3948 + 0.2100i 1.1310 - 0.4500i
0.2783 + 0.0889i 2.5500 + 0.2546i

>> A^2

ans =

9.0000 +31.4159i 81.6814 + 8.8858i
-7.0711 +65.0000i 98.0000 +59.7002i

>> A'

ans =

3.0000 + 0.0000i 0.0000 - 5.0000i
6.2832 + 0.0000i 10.0000 - 1.4142i

>> B^-1

ans =

0.0000 - 0.0817i 0.0681 + 0.0000i
0.0000 + 0.0285i 0.0318 + 0.0000i

>> B'*A'

ans =

1.0e+02 *

0.3948 - 0.2100i 0.2783 - 0.0889i
1.1310 + 0.4500i 2.5500 - 0.2546i

>> A^2 + B^2 - A*B

ans =

1.0e+02 *

-0.7948 - 0.8383i 0.7358 - 2.1611i
0.7819 + 1.0010i 1.6700 - 0.6000i

>>

(3)

Command Window >> A = [0.5 -0.8; 0.75 1.0]; >> [V, D] = eig(A); >> Colum of V represents each eigenvectors >> digonal elements of D represents respective eigenvalues >> eigVect_1 = V(:,1) value eigvect_1 = 0.7184 + 0.0000i -0.2245 - 0.6584i >> eigVect_2 = V(:,2) eigVect_2 = 0.7184 + 0.0000i -0.2245 + 0.6584i >> Scorresponding eigenvalues >> eigValues = diag (D) eigValues = 0.7500 + 0.733li 0.7500 - 0.733li fx >>|

Command Window >> A = [8 3; -34); >> [V, D] = eig(A); >> Colum of V represents each eigenvectors >> digonal elements of D represents respective eigenvalues >> eigvect_1 = V(:,1) eigVect_1 = 0.7071 + 0.0000i -0.4714 + 0.5270i >> eigVect_2 = V(:,2) eigVect_2 = 0.7071 + 0.0000i -0.4714 - 0.5270i >> eigValues = diag (D) eigValues = 6.0000 + 2.236li 6.0000 - 2.236li fx >> |

(4)

Command Window >> A = [5 5 -3; -1 2 3; 2 5 7]; >> [V, D] = eig(A); >> $ Eigen values >> EigValues = diag (D) EigValues = 2.5332 + 1.8225i 2.5332 - 1.8225i 8.9335 + 0.0000i >> $corresponding eigenvectors >> $ eigenvector i >>> eigVecl = V(:,1) eigVecl = 0.8787 + 0.0000i -0.3728 + 0.2064i 0.1012 - 0.1898i >> $ 2nd eigenvecotr >> eigVec2 = V(:,2) eigVec2 = 0.8787 + 0.0000i -0.3728 - 0.2064i 0.1012 + 0.1898i >> eigenvector 3 >> eigVec3 = V(:3) eigVec3 = V(:3) Error: Unexpected MATLAB expression. >> eigVec3 = V(:,3)

Command Window >> B = [1 2 3; 89 6; 5 3 -1]; >> [V, D] = eig (B); >> $ Eigen values >> EigValues = diag (D) EigValues = 12.8161 0.2675 -4.0836 >> Scorresponding eigenvectors >> $ eigenvector i >> eigVecl = V(:,1) eigVecl = -0.2299 -0.9305 -0.2852 >> $2nd eigenvecotr >> eigVec2 = V(:,2) eigVec2 = -0.5452 0.7528 -0.3688 >> $ eigenvector 3 >> eigVec3 = V(:,3) eigVec3 = -0.4718 -0.1126 0.8745

(5)

Command Window >> A = [1 2 3 5; -2 5 7-9; 5 >> B = [21; 17; 23; 26]; >> X = AB 7 2 -5; -1 -3 -7 7]; x = -8.0756 12.8353 -4.6128 3.4487 >> $(b) >> A = [1 -2 3 4; 2 -2 -1 1; 1-3 4-4; 2 2 -3 4]; >> B = [9; -5; 7; -6]; >> AB ans = -0.3822 0.8691 3.0157 0.5183 fx > |