Recent content by chrisb93

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    Proving Equality of Image and Eigenspace for Eigenvalue 1

    I don't see how that works, if x=y then Ax=x therefore (A+I)x=Ax+x=2x=y which contradicts itself.
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    Proving Equality of Image and Eigenspace for Eigenvalue 1

    It's never specifically defined in the question but I believe the subscript is the matrix representing the map so L(x) = (I_{n} + A)x
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    Determine whether the given vectors form a basis

    In echelon form I get \left( \begin{matrix} 1 & -2 & -3 \\ 0 & 5 & 8 \\ 0 & 0 & 0 \end{matrix} \right) Also be careful with difference between echelon form and reduced echelon form. The matrix you wrote (and the one above) is in echelon form, as every pivot has only zeros below it...
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    Determine whether the given vectors form a basis

    What makes you think they are lineally independent?
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    Proving Equality of Image and Eigenspace for Eigenvalue 1

    Homework Statement It's given or I've already shown in previous parts of the question: A \in M_{nxn}(F)\\ A^{2}=I_{n}\\ F = \mathbb{Q}, \mathbb{R} or \mathbb{C}\\ ker(L_{I_{n}+A})=E_{-1}(A) Eigenvalues of A must be \pm1 Show im(L_{I_{n}+A})=E_{1}(A) where E is the eigenspace for the eigenvalue...
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    Is there a simpler way to calculate this limit?

    Thanks so much, never thought of doing that to simplify limits.
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    Is there a simpler way to calculate this limit?

    Yes it is
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    Is there a simpler way to calculate this limit?

    Homework Statement \lim_{x\to\infty} \frac{(1 - 2x^3)^4}{(x^4 - x^3+1)^3} Homework Equations Not really applicable The Attempt at a Solution After applying L'Hospital's rule 3 times I could just see it getting untidy and I couldn't see my and mistakes in my working so I checked against...