Question

If v is a characteristic vector of n×n matrix A with the charact. value of r,...

If v is a characteristic vector of n×n matrix A with the charact. value of r, show that v is a charac. vector of A^2 -3A + 5I. what is the charac. value?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let A be an n × n matrix, v a column vector, and suppose {v, Av,...
Let A be an n × n matrix, v a column vector, and suppose {v, Av, . . . , An−1v} is linearly independent. Prove that if B is any matrix that commutes with A, then B is a polynomial in A.
Let V be a vector subspace of R^n for some n?N. Show that if k>dim(V) then...
Let V be a vector subspace of R^n for some n?N. Show that if k>dim(V) then the set of any k vectors in V is dependent.
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar...
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar multiplication is a finite dimensional vector space with dim GLm,n(R) = mn. Show that if V and W be finite dimensional vector spaces with dim V = m and dim W = n, B a basis for V and C a basis for W then hom(V,W)-----MatB--->C(-)--------> GLm,n(R) is a bijective linear transformation. Hence or otherwise, obtain dim hom(V,W). Thank you!
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉...
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉 ∈ R for x, y ∈ V . (a) (3points) Let λ∈R with λ>0. Show that 〈x,y〉′ = λ〈x,y〉, for x,y ∈ V, (b) (2 points) Let T : V → V be a linear operator, such that 〈T(x),T(y)〉 = 〈x,y〉, for all x,y ∈ V. Show that T is one-to-one. (c) (2 points) Recall that the norm of a vector x ∈ V...
Suppose we have a vector space V of dimension n. Let R be a linearly independent...
Suppose we have a vector space V of dimension n. Let R be a linearly independent set with order n−2. Let S be a spanning set with order n+ 2. Outline a strategy to extend R to a basis for V. Outline a strategy to pare down S to a basis for V .
Let E be an n×n matrix, and letU= {xE:x∈Rn} (where x∈Rn is written as arow vector)....
Let E be an n×n matrix, and letU= {xE:x∈Rn} (where x∈Rn is written as arow vector). Show that the following are equivalent. (a) E^2 = E = E^T (T means transpose). (b) (u − uE) · (vE) = 0 for all u, v ∈ Rn. (c) projU(v) = vE for all v ∈ Rn.
(Linear Algebra) A n×n-matrix is nilpotent if there is a "r" such that Ar is the...
(Linear Algebra) A n×n-matrix is nilpotent if there is a "r" such that Ar is the nulmatrix. 1. show an example of a non-trivial, nilpotent 2×2-matrix 2.let A be an invertible n×n-matrix. show that A is not nilpotent.
Let A be an m×n matrix, x a vector in Rn, and b a vector in...
Let A be an m×n matrix, x a vector in Rn, and b a vector in Rm. Show that if x1 in Rn is a solution to Ax=b and x2 is a solution to Ax=⃗0, then x1 +x2 is a solution to Ax=b.
Suppose V is a vector space over F, dim V = n, let T be a...
Suppose V is a vector space over F, dim V = n, let T be a linear transformation on V. 1. If T has an irreducible characterisctic polynomial over F, prove that {0} and V are the only T-invariant subspaces of V. 2. If the characteristic polynomial of T = g(t) h(t) for some polynomials g(t) and h(t) of degree < n , prove that V has a T-invariant subspace W such that 0 < dim W < n
Consider the ordered bases B={[8,9]} and C={[-2,0],[-3,3]} for the vector space R^2. A. find the matrix...
Consider the ordered bases B={[8,9]} and C={[-2,0],[-3,3]} for the vector space R^2. A. find the matrix from C to B. B.Find the coordinates of u=[2,1] in the ordered basis B. C.Find the coordinates of v in the ordered basis B if the coordinate vector of v in C =[-1,2].
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT