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Recent questions tagged vector-space
1
vote
0
answers
1
TIFR CSE 2022 | Part B | Question: 15
Let $\mathbb{R}$ denote the set of real numbers. Let $d \geq 4$ and $\alpha \in \mathbb{R}$ ... $\left(a_0, a_1, \ldots, a_d\right) \in S$, the function $ x \mapsto \sum_{i=0}^d a_i x^i $ has a local optimum at $\alpha$
admin
asked
in
Linear Algebra
Sep 1
by
admin
78
views
tifr2022
linear-algebra
vector-space
0
votes
1
answer
2
NIELIT 2017 DEC Scientist B - Section B: 20
Let $u$ and $v$ be two vectors in $R^2$ whose Eucledian norms satisfy $\mid u\mid=2\mid v \mid$. What is the value $\alpha$ such that $w=u+\alpha v$ bisects the angle between $u$ and $v$? $2$ $1$ $\dfrac{1}{2}$ $-2$
Lakshman Patel RJIT
asked
in
Numerical Methods
Mar 30, 2020
by
Lakshman Patel RJIT
297
views
nielit2017dec-scientistb
non-gate
vector-space
0
votes
0
answers
3
TIFR CSE 2020 | Part A | Question: 3
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f'_{a}(w) = 0\},$ where the polynomial function $f_{a}(x)$ ... $d$-dimensional vector subspace of $\mathbb{R}^{d+1}$ $S$ is a $(d-1)$-dimensional vector subspace of $\mathbb{R}^{d+1}$ None of the other options
Lakshman Patel RJIT
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Patel RJIT
468
views
tifr2020
engineering-mathematics
linear-algebra
vector-space
1
vote
2
answers
4
ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$
Sayan Bose
asked
in
Linear Algebra
May 6, 2019
by
Sayan Bose
1.5k
views
isi2019-mma
engineering-mathematics
linear-algebra
vector-space
non-gate
0
votes
0
answers
5
Vector Space
https://gateoverflow.in/18503/tifr2010-a-11 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
srestha
asked
in
Set Theory & Algebra
Sep 30, 2018
by
srestha
445
views
discrete-mathematics
vector-space
0
votes
0
answers
6
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
srestha
asked
in
Linear Algebra
May 17, 2018
by
srestha
219
views
vector-space
engineering-mathematics
1
vote
1
answer
7
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 $||P{\vec{x}}||$
Prince Sindhiya
asked
in
Linear Algebra
Mar 4, 2018
by
Prince Sindhiya
1.2k
views
gate2008-ee
engineering-mathematics
matrix
vector-space
1
vote
2
answers
8
ISRO-DEC2017-10
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 $\dfrac{2}{5}$ $2$ $3$ $\dfrac{5}{2}$
gatecse
asked
in
Linear Algebra
Dec 17, 2017
by
gatecse
1.3k
views
isrodec2017
vector-space
26
votes
4
answers
9
GATE CSE 2017 Set 1 | Question: 30
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ 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 $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$
Arjun
asked
in
Linear Algebra
Feb 14, 2017
by
Arjun
10.7k
views
gatecse-2017-set1
linear-algebra
normal
vector-space
2
votes
0
answers
10
TIFR CSE 2016 | Part B | Question: 6
A subset $X$ of $\mathbb{R}^n$ is convex if for all $x, y \in X$ and all $\lambda \in (0, 1)$, we have $\lambda x + (1- \lambda)y \in X$. If $X$ is a convex set, which of the following statements is necessarily TRUE? For every $ x \in X$ ... $x \in X$, then $\lambda x \in X$ for all scalars $\lambda$ If $x, y \in X$, then $x-y \in X$
go_editor
asked
in
Linear Algebra
Dec 28, 2016
by
go_editor
294
views
tifr2016
linear-algebra
vector-space
non-gate
3
votes
1
answer
11
TIFR CSE 2016 | Part A | Question: 3
Consider the following set of $3n$ linear equations in $3n$ ... $\mathbb{R}^{3n}$ of dimension n $S$ is a subspace of $\mathbb{R}^{3n}$ of dimension $n-1$ $S$ has exactly $n$ elements
go_editor
asked
in
Linear Algebra
Dec 26, 2016
by
go_editor
324
views
tifr2016
linear-algebra
vector-space
non-gate
6
votes
2
answers
12
TIFR CSE 2017 | Part A | Question: 2
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 $a, \: b$ ... $a, \: b$? Choose from the following options. ii only i and ii iii only iv only iv and v
go_editor
asked
in
Linear Algebra
Dec 21, 2016
by
go_editor
1.2k
views
tifr2017
linear-algebra
vector-space
1
vote
0
answers
13
TIFR-2014-Maths-B-9
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
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
171
views
tifrmaths2014
vector-space
non-gate
1
vote
0
answers
14
TIFR-2014-Maths-B-8
Let $X$ be a non-empty 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
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
196
views
tifrmaths2014
vector-space
1
vote
0
answers
15
TIFR-2014-Maths-B-7
$X$ is a topological space of infinite cardinality which is homeomorphic to $X \times X$. Then $X$ is not connected $X$ is not compact $X$ is not homeomorphic to a subset of $R$ None of the above
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
161
views
tifrmaths2014
vector-space
non-gate
1
vote
0
answers
16
TIFR-2014-Maths-A-16
$X$ 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
makhdoom ghaya
asked
in
Linear Algebra
Dec 17, 2015
by
makhdoom ghaya
248
views
tifrmaths2014
linear-algebra
vector-space
non-gate
1
vote
0
answers
17
TIFR-2011-Maths-B-12
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.
makhdoom ghaya
asked
in
Linear Algebra
Dec 10, 2015
by
makhdoom ghaya
263
views
tifrmaths2011
vector-space
non-gate
1
vote
0
answers
18
TIFR-2011-Maths-A-23
The space of solutions of infinitely differentiable functions satisfying the equation $y" + y = 0$ is infinite dimensional.
makhdoom ghaya
asked
in
Linear Algebra
Dec 9, 2015
by
makhdoom ghaya
245
views
tifrmaths2011
vector-space
non-gate
1
vote
0
answers
19
TIFR-2011-Maths-A-18
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 $3$.
makhdoom ghaya
asked
in
Linear Algebra
Dec 9, 2015
by
makhdoom ghaya
265
views
tifrmaths2011
vector-space
non-gate
3
votes
1
answer
20
TIFR2010-Maths-B-2
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
makhdoom ghaya
asked
in
Linear Algebra
Oct 11, 2015
by
makhdoom ghaya
1.4k
views
tifrmaths2010
vector-space
8
votes
1
answer
21
TIFR CSE 2010 | Part A | Question: 11
The length of a vector $X = (x_{1},\ldots,x_{n})$ is defined as $\left \| X\right \| = \sqrt{\sum \limits^{n}_{i=1}x^{2}_{i}}$ Given two vectors $X=(x_{1},\ldots, x_{n})$ and $Y=(y_{1},\ldots, y_{n})$, which of the following measures of ... $\left \| \frac{X}{\left \| X \right \|}-\frac{Y}{\left \| Y \right \|} \right \|$ None of the above
makhdoom ghaya
asked
in
Linear Algebra
Oct 3, 2015
by
makhdoom ghaya
1.0k
views
tifr2010
linear-algebra
vector-space
12
votes
2
answers
22
GATE CSE 1995 | Question: 2.13
A unit vector perpendicular to both the vectors $a=2i-3j+k$ and $b=i+j-2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+j-k)$ $\frac{1}{3} (i-j-k)$ $\frac{1}{\sqrt{3}} (i+j-k)$
Kathleen
asked
in
Linear Algebra
Oct 8, 2014
by
Kathleen
2.8k
views
gate1995
linear-algebra
normal
vector-space
28
votes
2
answers
23
GATE CSE 2014 Set 3 | Question: 5
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 _____.
go_editor
asked
in
Linear Algebra
Sep 28, 2014
by
go_editor
8.1k
views
gatecse-2014-set3
linear-algebra
vector-space
normal
numerical-answers
28
votes
4
answers
24
GATE CSE 2007 | Question: 27
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... 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
Kathleen
asked
in
Linear Algebra
Sep 22, 2014
by
Kathleen
12.1k
views
gatecse-2007
linear-algebra
normal
vector-space
1
vote
1
answer
25
GATE CSE 1993 | Question: 02.3
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 ________
Kathleen
asked
in
Linear Algebra
Sep 13, 2014
by
Kathleen
823
views
gate1993
linear-algebra
normal
vector-space
out-of-gate-syllabus
fill-in-the-blanks
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