Recent content by Jennifer1990

Homework Statement Let f(x, y) = x^2y^3 + xy. Is there a direction at (-1; 2) in which the rate of change of f is equal to 18? Justify your answer. Homework Equations The Attempt at a Solution plugging this into the directional derivative formula, i get 18 = -v1 + 13v2, where...

Homework Statement Is The space P2 is isomorphic to the space of all 3 × 3 diagonal matrices. Homework Equations The Attempt at a Solution I know that P2 is isomorphic to vectors with 3 components so i think this statement is true, is it?

A = [a b; c d] det (A) = ad-bc A transpose = [a c; b d] det A transpose = ad - bc = det A

lol that's funny. What i meant is May you show me such a proof, please?

ohhh it works o.o can i see a rigorous proof of this?

Homework Statement I don't understand why the determinant of a matrix is equal to its transpose...how is this possible? Homework Equations The Attempt at a Solution

ohhhhh is it m - n?

Homework Statement Suppose that dim V = m and dim W = n with M>=n . If the linear map A : V -> W is onto, what is the dimension of its kernel? Homework Equations The Attempt at a Solution Onto, means that every vector in W has at least one pre-image therefore, the kernel can...

Homework Statement Six digits from the numbers 2, 3, 4, 5, 6, 7, 8 are chosen and arranged in a row without replacement. Find the probability that the digits 2 and 3 appear in the proper order but not consecutively Homework Equations The Attempt at a Solution i know that the...

I just tried several similar matrices but they all share the same eigenvector O.o Can i get an example where two similar matrices have different eigenvectors?

ohhh i see... since they can have the same eigenvalues, does this mean that the matrices can also have the same eigenvectors?

oh wait...B = P^-1 AP ...so what i said is wrong... how can i manipulate A P^-1 P to look like P^-1 AP?

Av = lambda v (AP^-1 P)v = lambda v Bv = lambda v i think?

what do u mean by the same characteristic equation?

Homework Statement Let A and B be similar matrices a)Prove that A and B have the same eigenvalues Homework Equations None The Attempt at a Solution Firstly, i don't see how this can even be possible unless the matrices are exactly the same :S