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Recent questions tagged linear-algebra
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GATE CSE 2024 | Set 2 | Question: 37
Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the following statements is/are TRUE? The determinant of $B$ is the negative of the ... If $A$ is symmetric, then $B$ is also symmetric If the trace of $A$ is zero, then the trace of $B$ is also zero
Arjun
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Linear Algebra
Feb 16
by
Arjun
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gatecse2024-set2
linear-algebra
multiple-selects
3
votes
7
answers
2
GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$
Arjun
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in
Linear Algebra
Feb 16
by
Arjun
2.5k
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gatecse2024-set1
linear-algebra
6
votes
1
answer
3
GATE CSE 2024 | Set 1 | Question: 39
Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$? There exist at least $m-n$ linearly independent solutions to this system There exist $m-n$ ... solution in which at least $m-n$ variables are $0$ There exists a solution in which at least $n$ variables are non-zero
Arjun
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in
Linear Algebra
Feb 16
by
Arjun
2.4k
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gatecse2024-set1
multiple-selects
linear-algebra
5
votes
1
answer
4
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 22
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following is/are always true? The rank of $A$ is 12. The ranks of $A$ and $B$ are ... . If $v$ is a vector such that $A v=0$ then $B v$ is also 0. The rank of $B$ is at most 11.
GO Classes
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in
Linear Algebra
Feb 5
by
GO Classes
304
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goclasses2024-mockgate-14
linear-algebra
rank-of-matrix
multiple-selects
1-mark
5
votes
2
answers
5
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 49
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$ no solutions for some but not all $\vec{p}$; exactly one solution for all other $\vec{p}$ exactly one solution for ... some $\vec{p}$, exactly one solution for some $\vec{p}$ and more than one solution for some $\vec{p}$
GO Classes
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Linear Algebra
Feb 5
by
GO Classes
473
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goclasses2024-mockgate-14
linear-algebra
system-of-equations
multiple-selects
2-marks
2
votes
2
answers
6
Memory Based GATE DA 2024 | Question: 4
Consider the matrix \[ \mathrm{M} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix} \] Find the value of \(|\mathrm{M}^2 + 12M|\).
GO Classes
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in
Linear Algebra
Feb 5
by
GO Classes
392
views
gate2024-da-memory-based
goclasses
linear-algebra
determinant
numerical-answers
0
votes
0
answers
7
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.
GO Classes
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in
Linear Algebra
Feb 5
by
GO Classes
190
views
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
0
votes
2
answers
8
Memory Based GATE DA 2024 | Question: 6
Consider the matrix \[ \begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix} \] What is the nature of the eigenvalues of the given matrix? Both eigenvalues are positive. One eigenvalue is negative. Eigenvalues are complex conjugate pairs. None of the above.
GO Classes
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Linear Algebra
Feb 5
by
GO Classes
216
views
gate2024-da-memory-based
goclasses
linear-algebra
eigen-value
0
votes
1
answer
9
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 \( \sum_{i=1}^5 \sigma_i \)?
GO Classes
asked
in
Linear Algebra
Feb 5
by
GO Classes
154
views
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
numerical-answers
0
votes
1
answer
10
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?
GO Classes
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Linear Algebra
Feb 5
by
GO Classes
92
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gate2024-da-memory-based
goclasses
linear-algebra
system-of-equations
0
votes
0
answers
11
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.
GO Classes
asked
in
Linear Algebra
Feb 5
by
GO Classes
95
views
gate2024-da-memory-based
goclasses
linear-algebra
vector-space
7
votes
1
answer
12
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 13
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ ... $\left(\begin{array}{r}1 \\ -1 \\ 0\end{array}\right)$ $\left(\begin{array}{r}9 \\ 10 \\ 11\end{array}\right)$
GO Classes
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in
Linear Algebra
Jan 28
by
GO Classes
525
views
goclasses2024-mockgate-13
goclasses
linear-algebra
matrix
1-mark
9
votes
2
answers
13
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
GO Classes
asked
in
Linear Algebra
Jan 28
by
GO Classes
447
views
goclasses2024-mockgate-13
goclasses
linear-algebra
eigen-vector
2-marks
0
votes
1
answer
14
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.
rajveer43
asked
in
Machine Learning
Jan 27
by
rajveer43
148
views
machine-learning
artificial-intelligence
statistics
probability
linear-algebra
7
votes
2
answers
15
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 $11.$
GO Classes
asked
in
Linear Algebra
Jan 21
by
GO Classes
560
views
goclasses2024-mockgate-12
goclasses
linear-algebra
rank-of-matrix
multiple-selects
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