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10. Let Qi be the number of inequivalent Jordan block structures that a 6 by 6 matrix with eigenv...
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q....
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q. - 0 otherwise, where 86 100 01-81-94 T < 1 Let Q = 1013 + IQ1 + 2(Qal + 3(Qal). Then T = 5 sin2(100Q) satisfies:-(A) 0 (B) 1 T < 2.
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q. - 0...
1. Let Q1 , Q2, Q3, Q4 be constants so that f(z) = z4 + Qiz? + Q2z? + Q32+ Q4 is the characterist...
just number 3
1. Let Q1 , Q2, Q3, Q4 be constants so that f(z) = z4 + Qiz? + Q2z? + Q32+ Q4 is the characteristic polynomial of the matrix 42 1576 9 15 21-58 19 A76 -58 234 80 L9 19 -80 201J Let Q = In(3 + IQ1 + 2lQal + 3IQal + 4IQal). Then T = 5sin"(100Q) satisfies:--(A) 2. Let Qi s Q2 S Qs S Q4 be the eigenvalues of the matrix A of Question...
1. Let Q1 = y(7), where y solves dy dx + 8x 2 = 5x, y(6)...
1. Let Q1 = y(7), where y solves dy dx + 8x 2 = 5x, y(6) = 4. Let Q = ln(3 + |Q1|). Then T = 5 sin2 (100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5. 2. Let Q1 = y(1), where y solves dy dx + 1.7y = 5e 1.2x...
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13...
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2 Q2l+3 Qsl). Then T-5sin (100Q) satisfies: -(A) 0ST<1.
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2...
5. (22 pts) Consider the three-commodity market model given by: Qi = 16 – 2p1 +...
5. (22 pts) Consider the three-commodity market model given by: Qi = 16 – 2p1 + 2p2 + P3 and Qi = 2p1 – 7 Q2 = 8+2p1 – P2 – P3 and Q2 = 4p2 – 4 Q% = 4+421 – P2 – 4p3 and Qs = 2p3 – 3 where Q4, Q and pi denote quantity demanded, quantity supplied and price of good i = 1, 2, 3, respectively. (a) What is the relationship among the three goods?...
Let Q1=x(1.1) ,Q2=x(1.2), Q3=x(1.3). Then Let Q= ln(3 +|Q1|+ 2|Q2|+ 3|Q3|), Then T= 5 sin2(100Q) 1)...
Let Q1=x(1.1) ,Q2=x(1.2), Q3=x(1.3). Then Let Q= ln(3 +|Q1|+ 2|Q2|+ 3|Q3|), Then T= 5 sin2(100Q) 1) where x=x(t) solves x′′+x= tan(t), x(0) = 1, x′(0) = 2 2) where x=x(t) solves x′′−x=te^t, x(0) = 1, x′(0) = 2. 3) where x=x(t) solves x′′−x=t^2, x(0) = 1, x′(0) = 2 4) where x=x(t) solves x′′−2x′+x=(e^t/2t), x(1) = 1, x′(1) = 2 Please show all steps and thank you!
Linear Algebra Problem! Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
13. Let f(a) = r lnx for > 0. Let Q. be the point of inflection...
13. Let f(a) = r lnx for > 0. Let Q. be the point of inflection of S. Let Q3 = (Q2) be the minimum of f(x) for r > 0. Let Q = ln(3 + IQ1| + 2 Q2 + 3|Q31). Then T = 5 sinº(1000) satisfies:- (A) O ST < 1. - (B) 1 ST <2.-(C) 2 ST <3. - (D) 3 <T<4. - (E) 4 ST55.
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
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...
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q. - 0 otherwise, where 86 100 01-81-94 T < 1 Let Q = 1013 + IQ1 + 2(Qal + 3(Qal). Then T = 5 sin2(100Q) satisfies:-(A) 0 (B) 1 T < 2.
9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q. - 0...
just number 3
1. Let Q1 , Q2, Q3, Q4 be constants so that f(z) = z4 + Qiz? + Q2z? + Q32+ Q4 is the characteristic polynomial of the matrix 42 1576 9 15 21-58 19 A76 -58 234 80 L9 19 -80 201J Let Q = In(3 + IQ1 + 2lQal + 3IQal + 4IQal). Then T = 5sin"(100Q) satisfies:--(A) 2. Let Qi s Q2 S Qs S Q4 be the eigenvalues of the matrix A of Question...
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2 Q2l+3 Qsl). Then T-5sin (100Q) satisfies: -(A) 0ST<1.
4. Let (Q1.Q2.Qs)T be the least squares solution of A(Q1,.Q2.Qs)T b, where r 3 -1 5 1 -1 -13 3 13 7 -5 -20 -10 13 3 L 16 13 -13J Let Q - In(3+ IQil+2...
5. (22 pts) Consider the three-commodity market model given by: Qi = 16 – 2p1 + 2p2 + P3 and Qi = 2p1 – 7 Q2 = 8+2p1 – P2 – P3 and Q2 = 4p2 – 4 Q% = 4+421 – P2 – 4p3 and Qs = 2p3 – 3 where Q4, Q and pi denote quantity demanded, quantity supplied and price of good i = 1, 2, 3, respectively. (a) What is the relationship among the three goods?...
Linear Algebra Problem!
Problem 4 (Jordan Canonical Form). Let A be a matrix in C6,6 whose Jordan Canonical form is given by ON OON JODODD JODOC JOOD 000000 E C6,6 ] O O O O O As we gradually give you more and more information about A below, fill in the blanks in J (and explain how you know the filled in values are correct). You may choose to order the Jordan blocks however you wish. Note: during the interview,...
13. Let f(a) = r lnx for > 0. Let Q. be the point of inflection of S. Let Q3 = (Q2) be the minimum of f(x) for r > 0. Let Q = ln(3 + IQ1| + 2 Q2 + 3|Q31). Then T = 5 sinº(1000) satisfies:- (A) O ST < 1. - (B) 1 ST <2.-(C) 2 ST <3. - (D) 3 <T<4. - (E) 4 ST55.
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
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...
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