9. Let Q1 S Q2 be the eigenvalues of the matrix A and Qs 1 if Qi is a defective eigenvalue and Q....
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...
Give T accurate to 2 decimal places
10. Let Qi be the number of inequivalent Jordan block structures that a 6 by 6 matrix with eigenvalues 1, 2, 2, 3, 3, 3 can have. Let Q2 be the number of inequivalent Jordan block structures that a 6 by 6 matrix with eigenvalues 1, 1, 2, 2, 3, 3 can have. Let Qs be the number of inequivalent Jordan block structures that a 6 by 6 matrix with eigenvalues 1, 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 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...
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!
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...
0 2 0 Q1) Let A = 1 3 2 2 0 a) Determine all eigenvalues of A. b) Determine the basis for each eigenspace of A c) Determine the algebraic and geometric multiplicity of each eigenvalue. Q2) Let aj, 02, 03, 04, agbe real numbers. Compute ai det 1 1 Q3) Determine all values of x E R such that matrix 4 0 3 х 2 5 A = is invertable. х 0 0 1 0 0 4 0
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False Save Answer Q2 Basis 5 Points Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False O True Q3 Computation 5 Points [ 1 Find the algebraic and geometric multiplicity of the unique eigenvalue of 1 1 Write your answer in the form [a, g] where...
Consider machine M (Q. Σ , Γ, δ, q1, qaccept, qreject), where Q ,{qi, q2, gs, qaccept, qreject}, Σ as follows: { 0.1 } , Γ { 0.1 U } , and the transition function δ is δ (qi. Ú)-(qreject, U, R) δ (qi, 0)-(P-0, R) -(Gaccept, Prove that M is NOT a decider Describe in mathematical terms the language A that M recognises, and verify 1. your answer, ie prove that A- L(M)
Consider machine M (Q. Σ ,...
4. Let Q1, Q2 be constants so that f(Q 10.5x + 11.5x) dx = Q2e10.52 + Q1x2 + C, where C is a constant of integration. Let Q = ln(3+IQ.1+2Q2l). Then T = 5 sinº(1000) satisfies:- (A) 0 <T <1. (B) 1 <T <2. - (C) 2 <T <3. - (D) 3<T<4. - (E) 4 <T<5.
Let 4-β 0 0 A=1 0 4-3 024-β where β > 0 is a parameter. (a) Find the eigenvalues of A (note the eigenvalues will be functions of β). (b) Determine the values of β for which the matrix A is positive definite. Determine the values of β for which the matrix A is positive semidefinite. (c) For each eigenvalue of A, find a basis for the corresponding eigenspace. (d) Find an orthonormal basis for R3 consisting of eigenvectors of...