Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Webpage for Linear Algebra
Recent questions tagged linear-algebra
0
votes
1
answer
61
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
205
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
numerical-answers
+
–
0
votes
1
answer
62
Memory Based GATE DA 2024 | Question: 53
Consider the following scenarios involving linear algebra: For a \(3 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution? For a \(3 \times 3\) matrix, if some vector p ... 2 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution?
Consider the following scenarios involving linear algebra:For a \(3 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an in...
GO Classes
143
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
system-of-equations
+
–
0
votes
0
answers
63
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
139
views
GO Classes
asked
Feb 4
Linear Algebra
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
+
–
7
votes
1
answer
64
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 13
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ ... $\left(\begin{array}{r}1 \\ -1 \\ 0\end{array}\right)$ $\left(\begin{array}{r}9 \\ 10 \\ 11\end{array}\right)$
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ and $A\left(\begin{ar...
GO Classes
581
views
GO Classes
asked
Jan 28
Linear Algebra
goclasses2024-mockgate-13
goclasses
linear-algebra
matrix
1-mark
+
–
9
votes
2
answers
65
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 43
Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an eigenvector of $A?$ ... $\left[\begin{array}{l}1 \\ 1\end{array}\right]$. I only II only III only I and II only
Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an ...
GO Classes
509
views
GO Classes
asked
Jan 28
Linear Algebra
goclasses2024-mockgate-13
goclasses
linear-algebra
eigen-vector
2-marks
+
–
0
votes
1
answer
66
ML | DA Practice Questions
What is Error Analysis? (i) The process of analyzing the performance of a model through metrics such as precision, recall or F1-score. (ii) The process of scanning mis-classified examples to identify weaknesses of a model. (iii) The process ... to reduce the loss function during training. (iv) The process of identifying which parts of your model contributed to the error.
What is Error Analysis?(i) The process of analyzing the performance of a model through metrics such as precision, recall or F1-score.(ii) The process of scanning mis-clas...
rajveer43
185
views
rajveer43
asked
Jan 27
Machine Learning
machine-learning
artificial-intelligence
statistics
probability
linear-algebra
+
–
7
votes
2
answers
67
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 7
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. Which of the following is/are always true? The rank of $\text{A}$ ... that $\text{A} v=0$ then $\text{B} v$ is also $0.$ The rank of $\text{B}$ is at most $11.$
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. W...
GO Classes
635
views
GO Classes
asked
Jan 21
Linear Algebra
goclasses2024-mockgate-12
goclasses
linear-algebra
rank-of-matrix
multiple-selects
1-mark
+
–
4
votes
1
answer
68
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 30
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What are the maximum number of nonzero eigenvalues possible for the matrix $A?$
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What...
GO Classes
774
views
GO Classes
asked
Jan 13
Linear Algebra
goclasses2024-mockgate-11
goclasses
numerical-answers
linear-algebra
eigen-value
1-mark
+
–
5
votes
1
answer
69
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 36
Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are $m \times 1, m \times n$ ... $\operatorname{rank}[A]>$ $\operatorname{rank}[A \mid b]$.
Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are ...
GO Classes
515
views
GO Classes
asked
Jan 13
Linear Algebra
goclasses2024-mockgate-11
goclasses
linear-algebra
system-of-equations
multiple-selects
2-marks
+
–
0
votes
0
answers
70
Linear Transformation of Matrix
Debargha Mitra Roy
68
views
Debargha Mitra Roy
asked
Jan 12
Linear Algebra
linear-algebra
matrix
+
–
0
votes
1
answer
71
GATE 2016 | MATHS | Q-48
Let \( M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \) and \( e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots \). If \( e^M = [b_{ij}]\). then \[\frac{1}{e} \sum_{i=1}^{3} \sum_{j=1}^{3} b_{ij} \] is equal to ________________________
Let \( M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \) and \( e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots \). If \( e...
rajveer43
167
views
rajveer43
asked
Jan 11
Linear Algebra
linear-algebra
+
–
0
votes
0
answers
72
GATE 2016 | MATHS | QUESTION-47
Let \( A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} \) be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are \(\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix}\) respectively, then the value of \(3f\) is equal to ________________________
Let \( A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} \) be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are...
rajveer43
167
views
rajveer43
asked
Jan 11
Linear Algebra
linear-algebra
+
–
0
votes
0
answers
73
GATE 2016 | MATHS | Q-12
Consider the following statements P and Q: (P) : If \( M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} \), then M is singular. (Q) : Let S be a diagonalizable matrix. If T is a matrix such that \( ... ), then T is diagonalizable. Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q
Consider the following statements P and Q:(P) : If \( M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} \), then M is singular.(Q) : Let S be a diagon...
rajveer43
97
views
rajveer43
asked
Jan 11
Linear Algebra
linear-algebra
+
–
0
votes
0
answers
74
GATE 2016 | MATHS | Q-14
Consider a real vector space \( V \) of dimension \( n \) and a non-zero linear transformation \( T: \mathbb{V} \rightarrow \mathbb{V} \). If \( \text{dim}(T) < n \) and $T^2 = \lambda T$, for some \( \lambda \in \mathbb{R} \backslash \{0\} \), then which ... 0 \) for all \( X \in \mathbb{W} \) (C) \( T \) is invertible (D) \( \lambda\) is the only eigenvalue of \( T \)
Consider a real vector space \( V \) of dimension \( n \) and a non-zero linear transformation \( T: \mathbb{V} \rightarrow \mathbb{V} \). If \( \text{dim}(T) < n \) and ...
rajveer43
84
views
rajveer43
asked
Jan 11
Linear Algebra
linear-algebra
+
–
Page:
« prev
1
2
3
4
5
6
7
8
...
28
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register