Compute det |sI - Ac| for any n if Ac is a state matrix in Control...
Compute det |sI - Ac| for any n if Ac is a state matrix in Control Canonical Form.
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Compute det |sI - Ac| for any n if Ac is a state matrix in Control...
Q1. Suppose that A is an n x n invertible matrix. (a) Show that det(A-1) =...
Q1. Suppose that A is an n x n invertible matrix. (a) Show that det(A-1) = (det(A))-. (b) Show that det(APA-1) = det(P) for any n x n matrix P.
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can be computed by a cof...
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can be computed by a cofactor expansion across the ith row of A, that is, det A H-1)adtAj Hint: Use induction on i, For the induction step from i to i+1, flip rows i and i+1 (How does this change the determinant?) and use the induction assumption.
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can...
step by step plz Example. For the given matrix below compute both det(A) and det (5.A)....
step by step plz
Example. For the given matrix below compute both det(A) and det (5.A). 025 A=|1 7 10 01 3
i dont understand this problem. please show how to solve all parts using MATLAB. thank you. State-Space Representation and Analysis csys canon(sys,type) compute a canonical state-space realization...
i dont understand this problem. please show how to solve all
parts using MATLAB. thank you.
State-Space Representation and Analysis csys canon(sys,type) compute a canonical state-space realization type 'companion': controllable canonical form type modal: modal canonical form poles of a system controllability matrix observability matrix eig(A) ctrb(A,B) obsv(A,C) -7 L-12 0 EX A 2C-ioD0 uestions () Define the system in the state-space form (2) Determine the stability of the system (3) Determine the controllability and the observability of the system....
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2,...
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2, r3), control w and output z. (a) Draw a dynamic diagram of system S2 (b) Express the equations for S1 and S2 in matrix from and determine whether each system is controllable, observable. (c) These two systems are connected in series with w-y. The resulting system is called S3. Write down the matrix form of the equation for S3...
Find det [sI - An], n is arbitrary: This was a question from my class that...
Find det [sI - An], n is arbitrary: This was a question from my class that I don't understand how to do. Please help! Thanks!
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-...
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A).
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix...
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J...
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J under each of the following assumptions (i) A has only eigenvalue namely 4 and dim N(A- 41) = 4. one (ii) dim N(A 21) = 5. (ii dim N(A -I) = 3 and dim N (A 31) 2. (iv) det(A I) = (1 - )2(2 - A)2 (3 - ) and dim N(A - I) dim N(A - 21) 1 (v) A5 0 and...
3. (a) For the following matrix A, compute the characteristic polynomial C(A) = det(A ?): A-1...
3. (a) For the following matrix A, compute the characteristic polynomial C(A) = det(A ?): A-1 1 (b) Find all eigenvalues of A, using the following additional information: This miatrix has exactly 2 eigenvalues. We denote these ??,A2, where ?1 < ?2. . Each Xi is an integer, and satisfies-2 < ?? 2. (c) Given an eigenvalue ?? of A, we define the corresponding eigenspace to be the nullspace of A-?,I; note that this consists of all eigenvectors corresponding to...
Q1. Suppose that A is an n x n invertible matrix. (a) Show that det(A-1) = (det(A))-. (b) Show that det(APA-1) = det(P) for any n x n matrix P.
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can be computed by a cofactor expansion across the ith row of A, that is, det A H-1)adtAj Hint: Use induction on i, For the induction step from i to i+1, flip rows i and i+1 (How does this change the determinant?) and use the induction assumption.
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can...
step by step plz
Example. For the given matrix below compute both det(A) and det (5.A). 025 A=|1 7 10 01 3
i dont understand this problem. please show how to solve all
parts using MATLAB. thank you.
State-Space Representation and Analysis csys canon(sys,type) compute a canonical state-space realization type 'companion': controllable canonical form type modal: modal canonical form poles of a system controllability matrix observability matrix eig(A) ctrb(A,B) obsv(A,C) -7 L-12 0 EX A 2C-ioD0 uestions () Define the system in the state-space form (2) Determine the stability of the system (3) Determine the controllability and the observability of the system....
Given the two dynamic systems S2 a ER Si has state r1, control u, and output y. S2 has state (x2, r3), control w and output z. (a) Draw a dynamic diagram of system S2 (b) Express the equations for S1 and S2 in matrix from and determine whether each system is controllable, observable. (c) These two systems are connected in series with w-y. The resulting system is called S3. Write down the matrix form of the equation for S3...
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove that det ((-A-t +1 where t = Tr(A).
44. a.Let A and B be two 2 × 2 matrices,Let Tr denote the trace and det denote the determinant. Prove that Tr(AB)-Tr(BA) and det(AB) - det(BA). b. If A is any matrix in SLa(R), prove...
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J under each of the following assumptions (i) A has only eigenvalue namely 4 and dim N(A- 41) = 4. one (ii) dim N(A 21) = 5. (ii dim N(A -I) = 3 and dim N (A 31) 2. (iv) det(A I) = (1 - )2(2 - A)2 (3 - ) and dim N(A - I) dim N(A - 21) 1 (v) A5 0 and...
3. (a) For the following matrix A, compute the characteristic polynomial C(A) = det(A ?): A-1 1 (b) Find all eigenvalues of A, using the following additional information: This miatrix has exactly 2 eigenvalues. We denote these ??,A2, where ?1 < ?2. . Each Xi is an integer, and satisfies-2 < ?? 2. (c) Given an eigenvalue ?? of A, we define the corresponding eigenspace to be the nullspace of A-?,I; note that this consists of all eigenvectors corresponding to...
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