- multivariable calculus - How to efficiently determine $f_ {yx} (0,0 . . .
I could perform a similar computation to determine f′′yx(0, 0) f y x ″ (0, 0), but it feels rather cumbersome I know that if f′′xy f x y ″ and f′′yx f y x ″ are continuous at (0, 0) (0, 0), then their values at that point would be equal
- For $x,y \\in G$ prove that $xy=yx$ if and only if $y^{-1}xy=x$ if and . . .
These all work in the same manner, so I will just show one of these as a sample, say C A C A: y−1xy = x y(y−1xy) = yx (yy−1)xy = yx xy = yx y 1 x y = x y (y 1 x y) = y x (y y 1) x y = y x x y = y x The other two implications are very similar in nature
- abstract algebra - If $xy=yx$ in group $G$, then $ (xy)^n=x^ny^n . . .
2 To finish the inductive step, ykx =yk−1(yx) = (yk−1x)y = xyk−1y = xyk y k x = y k 1 (y x) = (y k 1 x) y = x y k 1 y = x y k As this is a low quality question, I will add my two cents into how to think about these operations Since groups are associative and commutative, we can just rearrange the variables in any order we want
- linear algebra - Rank of $xy^ {\mathrm T}+yx^ {\mathrm T . . .
Suppose that x ∈ Rn x ∈ R n and y ∈Rn y ∈ R n The matrices xyT x y T and yxT y x T are both of rank 1 1 Is the sum of these two matrices of rank 1 1, i e is the matrix xyT + yxT x y T + y x T of rank 1 1? I think the answer is positive and I am trying to come up with an argument that shows that this is true In general,
- How prove this $XY=YX$ - Mathematics Stack Exchange
How prove this XY = YX X Y = Y X Ask Question Asked 11 years, 6 months ago Modified 11 years, 6 months ago
- linear algebra - Finding matrices $X,Y$ such that $XY - YX = \left . . .
Finding matrices X, Y X, Y such that XY − YX = [011 101 110] X Y Y X = [0 1 1 1 0 1 1 1 0] Ask Question Asked 4 years, 10 months ago Modified 2 years, 4 months ago
- Prove that $yx = qxy$ implies $(x + y)^d = x^d + y^d. $
Here is the question I am trying to prove: Let q ≠ 1 q ≠ 1 be a root of unity of order d> 1 d> 1 Prove that yx = qxy y x = q x y in a noncommutative algebra implies
- algebra precalculus - Proving $x^n - y^n = (x-y) (x^ {n-1} + x^ {n-2} y . . .
Is there something I can do with xn +x2yn−2 −xn−2y2 −yn x n + x 2 y n 2 x n 2 y 2 y n that I'm not seeing, or did I make a mistake early on? EDIT: I should have pointed out that this exercise is meant to be done using nine of the twelve basic properties of numbers that Spivak outlines in his book: Associate law for addition Existence of an additive identity Existence of additive
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