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Recent questions tagged vectorspace
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Vector Space
https://gateoverflow.in/18503/tifr2010a11 Here how points are taken and and calculation has been done? Can anybody tell me why (x,y) taking all decimal value? I am not getting , plz somebody explain
asked
Sep 30, 2018
in
Set Theory & Algebra
by
srestha
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(
112k
points)

35
views
discretemathematics
vectorspace
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votes
0
answers
2
Vector
https://www.youtube.com/watch?v=3SkCNpFOshk In this lecture , can somebody define in 2nd question why $X_{1}+X_{2}\notin V_{1}\cup V_{2}$? I cannot understand the proof
asked
May 17, 2018
in
Linear Algebra
by
srestha
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112k
points)

45
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vectorspace
engineeringmathematics
+1
vote
1
answer
3
Ee gate 2008
Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ is a real vector $[x_1,x_2]^T$ with length ${\vec{x}}$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of the following statements is correct? A. $P{\vec{x}}$ $\leq$ ${\vec{x}}$ where ... satisfies $P{\vec{x}}$ >${\vec{x}}$ D. No relationship can be established between${\vec{x}}$ and $P{\vec{x}}$
asked
Mar 4, 2018
in
Linear Algebra
by
Prince Sindhiya
Loyal
(
5.4k
points)

157
views
gate2008ee
engineeringmathematics
matrix
vectorspace
0
votes
2
answers
4
ISRODEC201710
If vectors $\vec{a}=2\hat{i}+\lambda \hat{j}+\hat{k}$ and $\vec{b}=\hat{i}2\hat{j}+3\hat{k}$ are perpendicular to each other, then value of $\lambda$ is $\dfrac{2}{5}$ $2$ $3$ $\dfrac{5}{2}$
asked
Dec 17, 2017
in
Linear Algebra
by
gatecse
Boss
(
16.1k
points)

844
views
isrodec2017
vectorspace
+14
votes
3
answers
5
GATE2017130
Let $u$ and $v$ be two vectors in R2 whose Euclidean norms satisfy $\left \ u \right \ = 2\left \ v \right \$. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ 1}{2}$
asked
Feb 14, 2017
in
Linear Algebra
by
Arjun
Veteran
(
414k
points)

4.7k
views
gate20171
linearalgebra
normal
vectorspace
+3
votes
1
answer
6
TIFR2017A2
For vectors $x, \: y$ in $\mathbb{R}^n$, define the inner product $\langle x, y \rangle = \Sigma^n_{i=1} x_iy_i$, and the length of $x$ to be $\ x \ = \sqrt{\langle x, x \rangle}$. Let $a, \: b$ be two vectors in $\mathbb{R} ^n$ ... $a, \: b$? Choose from the following options. ii only i and ii iii only iv only iv and v
asked
Dec 21, 2016
in
Linear Algebra
by
jothee
Veteran
(
97.7k
points)

216
views
tifr2017
linearalgebra
vectorspace
+1
vote
0
answers
7
TIFR2014MathsB9
Let $f : X \rightarrow Y$ be a continuous map between metric spaces. Then $f(X)$ is a complete subset of $Y$ if The space $X$ is compact The space $Y$ is compact The space $X$ is complete The space $Y$ is complete.
asked
Dec 17, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

57
views
tifrmaths2014
vectorspace
nongate
+1
vote
0
answers
8
TIFR2014MathsB8
Let $X$ be a nonempty topological space such that every function $f : X \rightarrow \mathbb{R}$ is continuous. Then $X$ has the discrete topology $X$ has the indiscrete topology $X$ is compact $X$ is not connected.
asked
Dec 17, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

83
views
tifrmaths2014
vectorspace
+1
vote
0
answers
9
TIFR2014MathsB7
$X$ is a topological space of infinite cardinality which is homomorphic to $X \times X$. Then $X$ is not connected $X$ is not compact $X$ is not homomorphic to a subset of $R$ None of the above.
asked
Dec 17, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

39
views
tifrmaths2014
vectorspace
nongate
+1
vote
0
answers
10
TIFR2014MathsA16
$X$ is a metric space. $Y$ is a closed subset of $X$ such that the distance between any two points in $Y$ is at most $1$. Then $Y$ is compact Any continuous function from $Y \rightarrow \mathbb{R}$ is bounded $Y$ is not an open subset of $X$ none of the above.
asked
Dec 17, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

126
views
tifrmaths2014
linearalgebra
vectorspace
nongate
+1
vote
0
answers
11
TIFR2011MathsB12
Let $S$ be a finite subset of $\mathbb{R}^{3}$ such that any three elements in $S$ span a two dimensional subspace. Then $S$ spans a two dimensional space.
asked
Dec 10, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

81
views
tifrmaths2011
vectorspace
nongate
+1
vote
0
answers
12
TIFR2011MathsA23
The space of solutions of infinitely differentiable functions satisfying the equation $y" + y = 0$ is infinite dimensional.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

88
views
tifrmaths2011
vectorspace
nongate
+1
vote
0
answers
13
TIFR2011MathsA18
Consider the map $T$ from the vector space of polynomials of degree at most $5$ over the reals to $R \times R$, given by sending a polynomial $P$ to the pair $(P(3), P' (3))$ where $P'$ is the derivative of $P$. Then the dimension of the kernel is $3$.
asked
Dec 9, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

69
views
tifrmaths2011
vectorspace
nongate
+3
votes
1
answer
14
TIFR2010MathsB2
If $V$ is a vector space over the field $\mathbb{Z}/5\mathbb{Z}$ and $\dim_{Z/5\mathbb{Z}}(V)=3$ then $V$ has. 125 elements 15 elements 243 elements None of the above.
asked
Oct 11, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

268
views
tifrmaths2010
vectorspace
+5
votes
1
answer
15
TIFR2010A11
The length of a vector $x = (x_{1},\ldots,x_{n})$ is defined as $\left \ x\right \ = \sqrt{\sum ^{n}_{i=1}x^{2}_{i}}$. Given two vectors $x=(x_{1},\ldots, x_{n})$ and $y=(y_{1},\ldots, y_{n})$, which of the following measures of discrepancy between $x$ ... $\left \ \frac{X}{\left \ X \right \}\frac{Y}{\left \ Y \right \} \right \$ None of the above.
asked
Oct 3, 2015
in
Linear Algebra
by
makhdoom ghaya
Boss
(
29.5k
points)

436
views
tifr2010
linearalgebra
vectorspace
+6
votes
1
answer
16
GATE19952.13
A unit vector perpendicular to both the vectors $a=2i2j+k$ and $b=1+j2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+jk)$ $\frac{1}{3} (ijk)$ $\frac{1}{\sqrt{3}} (i+jk)$
asked
Oct 8, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
52.1k
points)

947
views
gate1995
linearalgebra
normal
vectorspace
+14
votes
2
answers
17
GATE201435
If $V_1$ and $V_2$ are $4$dimensional subspaces of a $6$dimensional vector space $V$, then the smallest possible dimension of $V_1 \cap V_2$ is _____.
asked
Sep 28, 2014
in
Linear Algebra
by
jothee
Veteran
(
97.7k
points)

2.1k
views
gate20143
linearalgebra
vectorspace
normal
numericalanswers
+17
votes
4
answers
18
GATE200727
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above
asked
Sep 22, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
52.1k
points)

3.1k
views
gate2007
linearalgebra
normal
vectorspace
+1
vote
1
answer
19
GATE199302.3
If the linear velocity $\vec V$ is given by $\vec V = x^2y\,\hat i + xyz\,\hat j – yz^2\,\hat k$ The angular velocity $\vec \omega$ at the point $(1, 1, 1)$ is ________
asked
Sep 13, 2014
in
Linear Algebra
by
Kathleen
Veteran
(
52.1k
points)

189
views
gate1993
linearalgebra
normal
nongate
vectorspace
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