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Exercise1 Decide if these matrices are matrix equivalent 4 2 1. Find the canonical representative...
HW21 linear transformations transition matrices: Problem 4 Previous Problem Problem List Next Problem 1 point) Recall that similarity of matrices is an equivalence relation, that is, the relation is...
HW21 linear transformations transition matrices: Problem 4 Previous Problem Problem List Next Problem 1 point) Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. 1 -2 is similar to itself by finding a T such that A TAT Verify that A T= 0 We know that A and are similar since A P-1BP where P Verify that B~A by finding an S such that B- S-'AS Verity that AC by finding...
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e....
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
(1 point) A matrix A is said to be similar to a matrix B if there...
(1 point) A matrix A is said to be similar to a matrix B if there is an invertible matrix P such that B = PAP 1 Let A1, A2, and A3 be 3 x 3 matrices Prove that if A1 is similar to A2 and A2 is similar to A3, then A similar to A. Proof: Since A1 is similar to A2, for some invertible matrix P for some invertible matrix Q Since A2 is similar to A3 for...
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix...
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а) А — 1 0 1 -1 1 0 2 -2 (Ъ) А %— -2 -2 -4 -2 2 |3 0 7 0 5 0 7 0 3 (с) А %—
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а)...
Let A t be a continuous family of 2 × 2 matrices and let P t) be the matrix solution to the initi...
Let A t be a continuous family of 2 × 2 matrices and let P t) be the matrix solution to the initial value problem p for n x n matrices, but it's messier.) Show that A()P, P )-P-(The result can be proved detP(t) (detPo) exp(J0 TrA(s)ds How is this related to the Wronskian from second order differential equations? (Look back at your work on second order differential equations in mth165 or similar class, or look up the definition on...
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1...
could u help me for this one??
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix...
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1...
can I have the answer for (a)? thank u!!
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For...
1. Find a matrix A such that L(x) = A ∗ x for all x ∈...
1. Find a matrix A such that L(x) = A ∗ x for all x ∈ R³ .What
is the relation between A and the matrix representation eLe of L
with respect to the standard bases for R³and R∧4?
2.
3. Compute the matrix representative eLS of .
Let L : R3 → R4 be the linear transformation given by L 22 23 [(3x1 – 2x2 – 7x3)] (5x1 – 3x3) (4x2 – 3x3) [(6x1 + 2x2 – 3x3) Let...
Problem 3 [10pts] Decide whether the following matrices are equivalent. (Justify your answer) / 5 -2...
Problem 3 [10pts] Decide whether the following matrices are equivalent. (Justify your answer) / 5 -2 -10 -9 3 1 1 0 0 -9 3 ) 4 1 -4 2 8 1 0 1 0 2 8 A= -1 0 2 1 -3 . 0 0 2 1 -3 | -3 0 7 3 0 0 0 0 0 0 J, B= ONO O
The transition matrix of a Markow chan s={1, 2, 3, 4, 5} is given by: ro.5...
The transition matrix of a Markow chan s={1, 2, 3, 4, 5} is given by: ro.5 0.5 ooo7 1 0.25 0.75 0 0 0 1 0.2 0.2 0.2 0.2 0.2 10.25 0.25 0.25 0.25 LO 0 0 0 1 A) Determine equivalence classes B) For each class determine its perlod city, and if their states are cument or transient c) Calculate P{Xi2 =2 / X 16-4}
HW21 linear transformations transition matrices: Problem 4 Previous Problem Problem List Next Problem 1 point) Recall that similarity of matrices is an equivalence relation, that is, the relation is reflexive, symmetric and transitive. 1 -2 is similar to itself by finding a T such that A TAT Verify that A T= 0 We know that A and are similar since A P-1BP where P Verify that B~A by finding an S such that B- S-'AS Verity that AC by finding...
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
(1 point) A matrix A is said to be similar to a matrix B if there is an invertible matrix P such that B = PAP 1 Let A1, A2, and A3 be 3 x 3 matrices Prove that if A1 is similar to A2 and A2 is similar to A3, then A similar to A. Proof: Since A1 is similar to A2, for some invertible matrix P for some invertible matrix Q Since A2 is similar to A3 for...
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а) А — 1 0 1 -1 1 0 2 -2 (Ъ) А %— -2 -2 -4 -2 2 |3 0 7 0 5 0 7 0 3 (с) А %—
1. For each of the following symmetric matrices, find an orthogonal matrix P and diagonal matrix D such that PTAP = D. 0 1 (а)...
Let A t be a continuous family of 2 × 2 matrices and let P t) be the matrix solution to the initial value problem p for n x n matrices, but it's messier.) Show that A()P, P )-P-(The result can be proved detP(t) (detPo) exp(J0 TrA(s)ds How is this related to the Wronskian from second order differential equations? (Look back at your work on second order differential equations in mth165 or similar class, or look up the definition on...
could u help me for this one??
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix...
can I have the answer for (a)? thank u!!
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For...
1. Find a matrix A such that L(x) = A ∗ x for all x ∈ R³ .What
is the relation between A and the matrix representation eLe of L
with respect to the standard bases for R³and R∧4?
2.
3. Compute the matrix representative eLS of .
Let L : R3 → R4 be the linear transformation given by L 22 23 [(3x1 – 2x2 – 7x3)] (5x1 – 3x3) (4x2 – 3x3) [(6x1 + 2x2 – 3x3) Let...
Problem 3 [10pts] Decide whether the following matrices are equivalent. (Justify your answer) / 5 -2 -10 -9 3 1 1 0 0 -9 3 ) 4 1 -4 2 8 1 0 1 0 2 8 A= -1 0 2 1 -3 . 0 0 2 1 -3 | -3 0 7 3 0 0 0 0 0 0 J, B= ONO O
The transition matrix of a Markow chan s={1, 2, 3, 4, 5} is given by: ro.5 0.5 ooo7 1 0.25 0.75 0 0 0 1 0.2 0.2 0.2 0.2 0.2 10.25 0.25 0.25 0.25 LO 0 0 0 1 A) Determine equivalence classes B) For each class determine its perlod city, and if their states are cument or transient c) Calculate P{Xi2 =2 / X 16-4}
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