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Sunday, February 5, 2023

Let m be the dim W.Â
$S=\{\alpha_1, \alpha_2, \alpha_3, ... , \alpha_m\}$ be the basis of subspace W.

Statement:Â Â
Let T be a linear operator on a finite dimensional vector space V. IfÂ f is the characteristic polynomial for T, Then f(T)=0, i.e....

Let (X, d) be a metric space and suppose that it is disconnected.
Claim: $\exists$ a non-empty proper subset of X which is both open & closed.
Since, X is disconnected by definition,Â $\exists$ non-empty sets A & B such that $X=A\cup B$, $\bar{A}\cap

Let (X, d) be a connected metric space and suppose that there exists a continuous functionÂ $f:X\to {\lbrace0, 1\rbrace}$.
Claim: f is constant.

Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? A. 25200 B....

Let $U$ and $V$ be two finite dimensional real vector spaces which are isomorphic.
i.e. $\exists$ a function $f:U\to V$ which is one-one, onto and linear transformation.

Statement:Â Â
Let T be a linear operator on a finite dimensional vector space V. IfÂ f is the characteristic polynomial for T, Then f(T)=0, i.e....

Question:A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and is left with Rs. 2Y and 2X paise. The...

Theorem:Â
Let V and W be two vector spaces on the same field. Let S and T be linear transformations from V into W. Then...

Theorem:Â
Every monotonic function on is Riemann integrable.
Proof:
Let â€‹( f:to mathbb{R} )â€‹ be monotonic function.
If f is constant function then obviously it is Riemann...

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