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location Canada
age 32
visits member for 2 years, 1 month
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I hold a diploma in Network Administration (along with many industry certifications) and am currently studying Computer Science and Pure Math in University.


Oct
22
answered Let $ABC$ be a well-defined product of matrices. Suppose that $A,C$ are both invertible. Prove that $rank(ABC)=rank(B)$.
Oct
22
comment Let $ABC$ be a well-defined product of matrices. Suppose that $A,C$ are both invertible. Prove that $rank(ABC)=rank(B)$.
@AgustíRoig Ahh.. I think I see how I might do this, then... If $A$ and $C$ are invertible, they can be reduced to $I$... and $I$ has the same rank as $A$ and $C$. So if I have the product $I_mBI_n$, then I get $B$...
Oct
22
comment Let $ABC$ be a well-defined product of matrices. Suppose that $A,C$ are both invertible. Prove that $rank(ABC)=rank(B)$.
@AgustíRoig What do you mean? "rank" is the dimension of the column space... so if $A$ and $C$ are invertible, and $A$ is an $m\times m$ matrix, then the columns of $A$ are linearly independent, meaning the dimensions of the column space is $m$, thus the rank of $A$ is $m$... simmilarly for $C$.
Oct
22
asked Let $ABC$ be a well-defined product of matrices. Suppose that $A,C$ are both invertible. Prove that $rank(ABC)=rank(B)$.
Oct
22
comment Multiplying matrices with left and right inverses
@BISHD Well, I never learned anything about the kernel... so I have no idea what to do with your suggestion, sorry
Oct
22
comment Multiplying matrices with left and right inverses
@BISHD There's no way I can determine this without knowing the components of the matrix... This is a general proof knowing only that the columns are linearly independent.
Oct
22
comment Multiplying matrices with left and right inverses
What is ker? I've never learned this term. Is it synonymous with the null space?
Oct
22
asked Multiplying matrices with left and right inverses
Oct
18
awarded  Popular Question
Oct
17
comment Need help with starting proof
That should read "$\exists n_{0}\in\mathbb{N},\ \forall n>n_{0},\ \epsilon<x_n<2\epsilon$."
Oct
17
comment Need help with starting proof
Is there any way to derive a value for $n_0$ from this $\epsilon$? I'm assuming not since we don't know (or care) what $x_n$ is... I'm just wondering if it's sufficient to say "Let $\epsilon=\min(L-a,b-L)$. Therefore, $\exists n_{0}\in\mathbb{N},\ \forall n>n_{0},\ |x_n|<\min(L-a,b-L)$."
Oct
16
comment Need help with starting proof
OK, I think I see it now - $b-L$ gives the distance between $L$ and $b$, likewise for $L-a$... So the minimum of the two is guaranteed to be within the interval $(a,b)$.
Oct
16
comment Need help with starting proof
I think so, not sure.
Oct
16
comment Need help with starting proof
I'm not sure I follow why we choose that $N(\epsilon)$...
Oct
16
asked Need help with starting proof
Oct
15
comment Calculate $\lim_{n\to\infty}\frac{1+a+a^2+\dots+a^n}{1+b+b^2+\dots+b^n}$
What if it evaluates to $\infty/\infty$? I was always told that this is not definitive, and might require L'Hopital's rule... It may converge and may not.
Oct
15
asked Calculate $\lim_{n\to\infty}\frac{1+a+a^2+\dots+a^n}{1+b+b^2+\dots+b^n}$
Oct
14
comment How to solve $9^{89}\equiv x\mod{1000}$ for $0\leq x\leq 999$ without calculating $9^{89}$
Is there any particular reason why you changed $(10-1)$ to $-(1-10)$?
Oct
14
accepted What is an intuitive definition of the zero vector?
Oct
14
accepted Construct a basis for $\mathbb{R}^4$ given two vectors and any two of the standard basis vectors in $\mathbb{R}^4$