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Search results for vector-space
30
votes
5
answers
1
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 $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$
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 $...
Arjun
14.0k
views
Arjun
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
normal
vector-space
+
–
0
votes
1
answer
2
Memory Based GATE DA 2024 | Question: 29
Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) are the singular values of \( M \), what is the value of \( \sum_{i=1}^5 \sigma_i \)?
Consider the vector \( u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} \), and let \( M = uu^{\top} \). If \( \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 \) ar...
GO Classes
204
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
numerical-answers
+
–
0
votes
0
answers
3
Memory Based GATE DA 2024 | Question: 5
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statements are true? \(M^3 = M\) \(M^2 = M\) The nullspace of \(M\) is 1-dimensional. The nullspace of \(M\) is 2-dimensional.
Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statement...
GO Classes
225
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
+
–
0
votes
0
answers
4
Memory Based GATE DA 2024 | Question: 60
Linear Algebra Question: Four options were given related to subspace R3. Something like this : A. \( \alpha \cdot x + \beta \cdot y \) B. \( \alpha^2 \cdot x + \beta^2 \cdot y \) C. \(f(x) = 4x_1 + 2x_3 + 3x_3 \) D.
Linear Algebra Question: Four options were given related to subspace R3.Something like this :A. \( \alpha \cdot x + \beta \cdot y \)B. \( \alpha^2 \cdot x + \beta^2 \cdot...
GO Classes
137
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
+
–
1
votes
1
answer
5
GATE 2018 | MATHS | Q-51
Consider \( \mathbb{R}^3 \) with the usual inner product. If \( d \) is the distance from \( (1, 1, 1) \) to the subspace ${(1, 1, 0), (0, 1, 1)}$ of \( \mathbb{R}^3 \), then \( 3d^2 \) is given by
Consider \( \mathbb{R}^3 \) with the usual inner product. If \( d \) is the distance from \( (1, 1, 1) \) to the subspace ${(1, 1, 0), (0, 1, 1)}$ of \( \mathbb{R}^3 \), ...
rajveer43
145
views
rajveer43
asked
Jan 11
Linear Algebra
linear-algebra
vector-space
+
–
0
votes
1
answer
6
GATE 2016 | MATHS | Q-11
Let \( \mathbf{v}, \mathbf{w}, \mathbf{u} \) be a basis of \( \mathbb{V} \). Consider the following statements P and Q: (P) : \( \{\mathbf{v} + \mathbf{w}, \mathbf{w} + \mathbf{u}, \mathbf{v} - \mathbf{u}\} \) is a basis of \( \mathbb{V} \). ( ... a basis of \( \mathbb{V} \). Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q
Let \( \mathbf{v}, \mathbf{w}, \mathbf{u} \) be a basis of \( \mathbb{V} \). Consider the following statements P and Q:(P) : \( \{\mathbf{v} + \mathbf{w}, \mathbf{w} + \m...
rajveer43
150
views
rajveer43
asked
Jan 11
Linear Algebra
vector-space
+
–
0
votes
0
answers
7
GATE 2018 | MATHS | Q-50
Let \( M_2(\mathbb{R}) \) be the vector space of all \( 2 \times 2 \) real matrices over the field \( \mathbb{R} \). Define the linear transformation \( S : M_2(\mathbb{R}) \to M_2(\mathbb{R}) \) by \( S(X) = 2X + X^T \), where \( X^T \) denotes the transpose of the matrix \( X \). Then the trace of \( S \) equals________
Let \( M_2(\mathbb{R}) \) be the vector space of all \( 2 \times 2 \) real matrices over the field \( \mathbb{R} \). Define the linear transformation \( S : M_2(\mathbb{R...
rajveer43
64
views
rajveer43
asked
Jan 11
Linear Algebra
linear-algebra
vector-space
+
–
0
votes
0
answers
8
GATE 2019 | Maths | DA Sample questions
Let $V$ be the vector space of all $3 \times 3$ matrices with complex entries over the real field. If $W_1 = \{A \in V : A = \bar{\mathbf{A}}^T \}$ and $W_2 = \{A \in V : trace(A)=0\}$, then the dimension of $W_1 + W_2$ is equal to ______________ ($\bar{\mathbf{A}}^T $ denotes the conjugate transpose of $A$.)
Let $V$ be the vector space of all $3 \times 3$ matrices with complex entries over the real field. If $W_1 = \{A \in V : A = \bar{\mathbf{A}}^T\}$ and $W_2 = \{A \in V : ...
rajveer43
112
views
rajveer43
asked
Jan 10
Linear Algebra
vector-space
linear-algebra
+
–
0
votes
0
answers
9
GATE 2021 | MATHS | PRACTICE PROBLEMS FOR DA PAPER
Let $ \langle \cdot, \cdot \rangle: \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R} $ be an inner product on the vector space $ \mathbb{R}^n $ over $ \mathbb{R} $. Consider the following statements: $P:$ ... P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE
Let $ \langle \cdot, \cdot \rangle: \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R} $ be an inner product on the vector space $ \mathbb{R}^n $ over $ \mathbb{R} $. Consid...
rajveer43
110
views
rajveer43
asked
Jan 10
Linear Algebra
linear-algebra
vector-space
+
–
13
votes
2
answers
10
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 18
In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ ... a element in matrix $\text{A}$ at $\mathrm{i}^{\text {th }}$ row and $\mathrm{j}^{\text{th}}$ column.
In this problem, consider the $4 \times 4$ matrix $A$ whose columns are vectors $\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3, \mathbf{a}_4 \in \mathbb{R}^4$ :$$A=\left[\math...
GO Classes
744
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
numerical-answers
goclasses
linear-algebra
matrix
vector-space
2-marks
+
–
4
votes
2
answers
11
TIFR CSE 2023 | Part B | Question: 5
Consider unit vectors $\mathbf{a}$ and $\mathbf{b}$ in $\mathbb{R}^{n}$. Let $\mathbf{w}$ be an arbitrary vector in $\mathbb{R}^{n}$ and $\eta$ be a positive real number such that \[ \mathbf{a}^{\mathbf{T}} \mathbf{b} \geq \eta>0 \geq \ ... $\text{(S3)}$ must be true, but statement $\text{(S2)}$ may be false. Statement $\text{(S1)}$ may be false.
Consider unit vectors $\mathbf{a}$ and $\mathbf{b}$ in $\mathbb{R}^{n}$. Let $\mathbf{w}$ be an arbitrary vector in $\mathbb{R}^{n}$ and $\eta$ be a positive real number ...
admin
381
views
admin
asked
Mar 14, 2023
Linear Algebra
tifr2023
linear-algebra
vector-space
+
–
4
votes
1
answer
12
TIFR CSE 2023 | Part A | Question: 3
$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. How many possible vectors $z$ exist, so that $A z=b?$ $0$ $1$ $n-1$ $n$ Either $0$ or infinite
$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. ...
admin
447
views
admin
asked
Mar 14, 2023
Linear Algebra
tifr2023
linear-algebra
vector-space
+
–
4
votes
0
answers
13
TIFR CSE 2023 | Part A | Question: 1
Let $A$ be a symmetric $3 \times 3$ matrix with real entries. Let $u$ and $v$ be non-zero vectors with real entries such that $A u=2 u$ and $A v=3 v$. From the set of values $\{0,1,-1\}$, which values can the inner product $u^{T} v$ take? $0$ only $1$ only $-1$ only All of the values $0,1$ and $-1$ None of the values $0,1$ and $-1$
Let $A$ be a symmetric $3 \times 3$ matrix with real entries. Let $u$ and $v$ be non-zero vectors with real entries such that $A u=2 u$ and $A v=3 v$. From the set of val...
admin
533
views
admin
asked
Mar 14, 2023
Linear Algebra
tifr2023
linear-algebra
vector-space
+
–
0
votes
0
answers
14
Linear Algebra, Vectors
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.
kidussss
309
views
kidussss
asked
Jan 13, 2023
Linear Algebra
linear-algebra
engineering-mathematics
vector-space
+
–
1
votes
0
answers
15
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 $\alpha$
Let $\mathbb{R}$ denote the set of real numbers. Let $d \geq 4$ and $\alpha \in \mathbb{R}$. Let$$ S=\left\{\left(a_0, a_1, \ldots, a_d\right) \in \mathbb{R}^{d+1}: \sum_...
admin
349
views
admin
asked
Sep 1, 2022
Linear Algebra
tifr2022
linear-algebra
vector-space
+
–
33
votes
4
answers
16
GATE CSE 2007 | Question: 27
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above
Consider the set of (column) vectors defined by$$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 \}$$.Which of the f...
Kathleen
16.5k
views
Kathleen
asked
Sep 21, 2014
Linear Algebra
gatecse-2007
linear-algebra
normal
vector-space
+
–
0
votes
1
answer
17
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 $v$? $2$ $1$ $\dfrac{1}{2}$ $-2$
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 bet...
admin
633
views
admin
asked
Mar 30, 2020
Numerical Methods
nielit2017dec-scientistb
non-gate
vector-space
+
–
3
votes
1
answer
18
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
Consider the following set of $3n$ linear equations in $3n$ variables:$\begin{matrix} x_1-x_2=0 & x_4-x_5 =0 & \dots & x_{3n-2}-x_{3n-1}=0 \\ x_2-x_3=0 & x_5-x_6=0 & & x_...
go_editor
547
views
go_editor
asked
Dec 26, 2016
Linear Algebra
tifr2016
linear-algebra
vector-space
non-gate
+
–
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