Please see the attached file for full problem description. ? Let . Compute the characteristic polynomial and all eigenvalues and all eigenvectors of A. ? True or false? Justify your answer in each case (giving a proof or a counterexample); Let be a linear transformation which is an isomorphism. Denote its inverse by
Please help me solve the following linear algebra questions involving linear transformation and matrices. (see attached) ? Let and let . Define a map by sending a vector to . a) let and be the standard basis vectors of V. let , and be the standard basis vectors of W. Find the matrix of T with respect to
In each of the attached cases show that the set U is linearly independent subset of the vector space V. Give, with justification, a basis of V which contains the set U.
1// Is it safe to state that for non linear system it's safe to assume/start off with x1 dot = x2? 2// The solutions to x1 dot and x2 dot are provided in the attached. I'm unsure how to arrive at said solutions and require assistance. Thanks in advance.
Use the minimax principle to show that the intermediate eigenvalue {see attachment} is not positive. *Please see attachment for eigenvalue and hint on how to complete the question. Thanks for your help.
Suppose that V and W are vector subspaces of Rn. If I define: V + W = {v+w: v belonging to V, w belonging to W} How can I prove that V+W is also a vector subspace of Rn and ALSO how could verify that (for example) <(1,0,1), (-1,0,1)> + <(3,2,1)> = R3 Thanks
Prove the following theory: 1) R1 is a subset of R2 => All of R3, R1R3 is a subset of R2R3 and 2) R1 is a subset of R2 => All of n, (R1)^n is a subset (R2)^n 3) Suppose R is transitive, then for all of n, R^n is a subset of R.
Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution. 1) Solve the system using elementary row operations on the equations of the augmented matrix. Fol
Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution. 1) The augmented matrix of a linear system has been transformed by row operations into the form be
The following linear trend equation was developed for the annual sales of the Jordan Manufacturing Company, Y1 = 500 + 60X (in $ of dollars). By how much per year and per month are sales increasing?
Basic operation research problem proof (Suppose x solves the problem....Let p,q be random variables with expected (mean) values etc) See attachment for details
Find the general solution ( if solution exist) of each of the following linear Diophantine equations: (a) 2x + 3y = 4 (d) 23x + 29y = 25 (b) 17x + 19y = 23 (e) 10x - 8y = 42 (c) 15x + 51y
In a linear system 2x + 3y =8 -x + 2y - z =0 3x +2 z=9 I am attempting to solve for x,y, and z using the Gaussian elimination with scaled partial pivoting. I also need to show intermediate matrices and vectors.
The Fermat numbers are numbers of the form 2 ^2n + 1 = Φn . Prove that if n < m , then Φn │ϕ m - 2. The Fermat numbers are numbers of the form 2 ^2n + 1 = (Phi)n . Prove that if n < m , then (Phi)n │(Phi)m - 2.
Linear dependence of vectors Linear independence of vectors Linear combinations of vectors
Find all solutions of each of the systems of congruences:- (a) x is congruent to 1 (mod 2) (d) 4x is congruent to 2 (mod 6) x is congruent to 2 (mod 3)
Z=sum of dots (uniform on {1,2,3,4,5,6} a. M_z(s)=? b. M_z(s)=M_x(s)^2 why? M_z stands for the mgf of x=sum of dots when two dice are tossed
Once you obtain eigenvalues of 8.248, 7.661, and -3.909 for the matrix 1 5 -3 5 4 2 -3 2 7 what are the next steps to obtain the eigenvectors.
Find the Eigenvalues and Eigenvectors of the following matrix 1 5 -3 5 4 2 -3 2 7
X^2 - 2xy - 3y^2 = 1 x - 2y = 2
Let A be a 4x4 matrix with minimal polynomial m(t)=(t^2 + 1)(t^2 - 3). Find the rational canonical form for A if A is a matrix over (a) the rational field Q (b)the real field R, (c) the complex field C.
Let T be a linear operator on a finite dimensional vector space V. Suppose the minimal polynomial for T is of the form P^n where p is an irreducible polynomial over the scalar field. Show that there is a vector x in V such that the T-annihilator of x is p^n.
1. Let V be a vector space of odd dimension (greater than 1) over the real field R. Show that any linear operator on V has a proper invariant subspace other than {0}.
If a subset A of a metric space X has diameter less than epsilon, then it can be covered with one open ball of radius epsilon. Prove. (We must use direct definitions only for the proof).
Show that the operator L defined by L[y](x) = ∫_o^1(x-t)^2ydt is a linear operator
Consider the perturbed linear system x' = (A + eB(t))x, x is an element of R^n, where A is a constant matrix, B is a bounded continuous matrix valued function, and e is a small parameter. Assume that all eigenvalues of A have non-zero real part. 1) Show that the only bounded solution of the system is 0. 2) If A ha
Please see file attached.
Prove the statements that are true and give counterexample to disprove those that are false. For all integers n, if n is prime then (-1)^n=-1 (READ:...then (-1) to the n power equal -1)
8x+3y= -4 3x+4y=10
Solve the system of equations. 2x+3y=5 3x+2y= -5