Brain Balance Mathematics

Two finite dimensional vector spaces over the same field are isomorphic iff they are of the same dimensions

First isomorphism theorem for vector space, homomorphism, kernel and isomorphism of vector space

Dimension theorem of a quotient space: If W be a subspace of a finite dimensional vector space V over ( mathbb{R} ) then (...

Dimension theorem of a quotient space: If W be a subspace...

Naresh Patkare - January 28, 2023 1

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

Cayley Hamilton Theorem

Naresh Patkare - February 1, 2023 0

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

40 Maths General Knowledge Questions And Answers

April 2, 2022

Two finite dimensional vector spaces over the same field are isomorphic...

January 31, 2023

$Find the value of $k$, for which $f(x)=begin{cases} frac{sqrt{1+kx}-sqrt{1-kx}}{x}, text{if} -1le x < 0 \ frac{2x+1}{x-1}, text{if} 0le x < 1 end{cases}$ is continuous at $x=0$$

Find the value of $k$, for which $f(x)=begin{cases} frac{sqrt{1+kx}-sqrt{1-kx}}{x}, text{if} ...

August 12, 2021

The product of 2 numbers is 1575 and their quotient is...

October 8, 2021

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Two finite dimensional vector spaces over the same field are isomorphic...

A metric space (X, d) is disconnected iff there exists a non-empty proper open...

Naresh Patkare - January 25, 2023 0

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, $\exists$ non-empty sets A & B such that $X=A\cup B$, $\bar{A}\cap

A metric space (X, d) is connected iff every continuous function is constant

Naresh Patkare - January 25, 2023 0

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

Out of 7 consonants and 4 vowels, how many words of 3 consonants and...

Naresh Patkare - October 8, 2021 0

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

Two finite dimensional vector spaces over the same field are isomorphic iff they are...

Naresh Patkare - January 31, 2023 0

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.

Cayley Hamilton Theorem

Naresh Patkare - February 1, 2023 0

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

A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and...

Naresh Patkare - September 23, 2021 2

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...

Linear Transformation Part I – Algebra of Linear Transformation

Naresh Patkare - May 30, 2021 0

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

Every monotonic function on [a, b] is Riemann integrable

Naresh Patkare - January 27, 2023 0

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