4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the givenmatrixexponentials.4 -1- ( 1 = ₂ ),!), f(t) =f(t) = (5-2(a) A =18e2t30e²t), x(0) = ( 0 ), e4t.At=1 (-e-t + 5e³t-5e-t +5e³te-t-e³t5e-te³t

Answered: Image /qna-images/answer/c2809860-46ab-4c44-8e74-1f8e22f27576.jpg

Answered: 4. Solve the non-homogeneous systems of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

If A is a 3 x 3 matrix and det(A) = -2 what is the determinant of (5A) A. 250 В. 1 250 С. 1 250 D. No correct answer E. -250
2. (a) Find the inverse of the matrix A. A = ( 1₂1 ) (b) Use your answer from (a) to find the solutions to the following system. You must use A-1 to find the solutions to get credit. x + y = 2 5x + 6y = 9
kindly answer it perfectly
1. for the case of repeated real roots what would the general solution be?2. if i was to let y1(t) = theta(t) as well as y2(t) = theta'(t)=y1'(t) how could i show that the initial equation could be written as a system of 1st order odes that involved y1 and y2. the system will then need to be presented as a the matrix equation y' = My
2. (a) Find the inverse of the matrix A. A = ( 1₂1 ) (b) Use your answer from (a) to find the solutions to the following system. You must use A-1 to find the solutions to get credit. x + y = 2 5x + 6y = 9
2x + 3y + 6z = 3 + 2y + 2z = −1 using 3x - 4y - 5z = -6 B. Solve the linear system-x 1. Cramer's rule 2. inverse matrix 3. LU decomposition
(4) Given matrix A = ( 2 −1 3 5 ) , and that h(T) = T 2 − 2T − 7, find h(T). ??????? ??? ? (1) A course repeater claims that his brother who did some Calculus at college years ago, but currently on some cough medication, believes that the first derivative of f(x) = (2x 2 − 1)(x 2 + 3) x 2 + 1 is f ′ (x) = [ 4x 2x 2 − 1 + 2x x 2 + 3 − 2x x 2 + 1 ][ (2x 2 − 1)(x 2 + 3) x 2 + 1 ] and that the first derivative of g(x) = (x 2 + 8) 7 (2 − 3x2) 5 is g ′ (x) = [ 14x x 2 + 8 + 30x 2 − 3x2 ] [ (x 2 + 8) 7 (2 − 3x2) 5 ] Using the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you confirm whether his brother is right, wrong or a little tipsy. (2) In the following triangle below, the degree measures of the three interior angles and two of the exterior angles are represented with variables and expressions. (a) Find the size of each of the interior angle.
For matrix A = '4 C ), if g(X) = X² + 4x + 2, what is the answer to g(A)? 3.
Theorem". The bisection approach is always Convergent proof we have | α-{\
1. 2. 3. For which values of a and b is the following system of equations inconsistent. x+2y3z = 4 3x = y + 5z = 2 4x + y + az = b (a) a= 2 and b = 6; (d) a = 1 and b = 3; (d) A = Find the standard matrix for the operator on R² which contracts with factor 1/4, then reflects about the line y = x. 0 (a) A = 1/4 0 (₁/11) ( 0 1/4 1/4 ¹/4) 0 (b) a = 2 and b = 6; (e) None of these. (c) a 2 and b = 6; 0 1/4 - (¹/4) 0 (e) None of these (b) A = (e) None of these (c) A = The linear operator T : R³ → R³ is defined by T(x₁, x2, X3) = (W₁, W2, W3), where w₁ = 2x₁ + 4x2 + x3; W₂ = 9x2+2x3; W3 = 2x1 8x2 - 2x3. Which of the following is correct. (a) T is not one to one. (b) T is one to one but the standard matrix for T-¹ does not exist. (c) T is one to one and its standard matrix for T-¹ is (d) T is one to one and its standard matrix for T-¹ is HOLI 0 1 (88) 0 3 0 1 3 3 WIN - WIN 3 0 1 3 1 -4 3 -3 2 -3 1623
2 (a) Given the matrices, A = (²5), and (i) 2A- 3B. (ii) (b) AB. (ii) Given the matrices, A = (₁2), find (i) det(A). and B = (²¹3), find A-¹. (c) Given that Q = (234) is a singular matrix. Find the value of k.

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

4. Solve the non-homogeneous systems of ODEs x' = Ax+f(t), with x(a) = xa using the given matrix exponentials. 4 - ( 1 =2), ), f(t) = ( ₁ 5 -2 (a) A = ), x(0) = ( 8 ), e¹² = ½ ( At 18e2t 30e²t -e +5e³t e-t-e³t -5e-t + 5e³t 5e-t-e³t