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1 votes
1 answer
332
Find the Eigen Vector
Find the Eigenvector of $\begin{bmatrix} 1 & cos\theta\\ cos \theta & 1 \end{bmatrix}$
Find the Eigenvector of $\begin{bmatrix} 1 & cos\theta\\ cos \theta & 1 \end{bmatrix}$
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11 votes
3 answers
334
ISI2016
Let $A$ be a matrix such that: $A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$ and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true? $B^{2}=I$ $B^{2}=0$ $B^{2}=B$ None of the above
Let $A$ be a matrix such that:$A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true?$B^{2}=I$$B^{2}=0$$B^...
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1 votes
1 answer
335
Gate 2013 IN What do you mean by dimension of null space?
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0 votes
1 answer
336
sparse matrix
How many real links are required to store a sparse matrix of 10 rows , 10 columns ,and 15 non zeros entries.(pick up the closest answer)
How many real links are required to store a sparse matrix of 10 rows , 10 columns ,and 15 non zeros entries.(pick up the closest answer)
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2 votes
5 answers
337
linearalgebra
if $A = \begin{bmatrix} 2 &3 &4 \\ 3 & -1 &2 \\ -1& 4 & 5 \end{bmatrix}$ then rank of the matrix $(A-A^T)$ is _____ (A) $1$ (B) $2$ (C) $3$ (D) $0$
if $A = \begin{bmatrix} 2 &3 &4 \\ 3 & -1 &2 \\ -1& 4 & 5 \end{bmatrix}$ then rank of the matrix $(A-A^T)$ is _____(A) $1$ (B) $2$ (C...
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0 votes
0 answers
339
groups
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0 votes
2 answers
340
Determinant of matrix
What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?
What is the determinant of matrix 2A. determinant of matrix A is 3. and IT is 4 by 4 matrix?
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1 votes
1 answer
341
Matrix multiplication 1
I want to ask about the equation i hv marked a question mark. (p-1qp)n=p-1qnp how?? Why is there no power on matrix p ?
I want to ask about the equation i hv marked a question mark.(p-1qp)n=p-1qnp how??Why is there no power on matrix p ?
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1 votes
2 answers
342
matrix
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0 votes
1 answer
343
matrix
how to solve??
how to solve??
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5 votes
2 answers
345
TIFR-2015-Maths-A-6
Let $A$ be the $2 \times 2$ matrix $\begin{pmatrix} \sin\frac{\pi}{18}&-\sin \frac{4\pi}{9} \\ \sin \frac{4\pi}{9}&\sin \frac {\pi}{18} \end{pmatrix}$. Then the smallest number $n \in \mathbb{N}$ such that $A^{n}=1$ is. $3$ $9$ $18$ $27$
Let $A$ be the $2 \times 2$ matrix $\begin{pmatrix}\sin\frac{\pi}{18}&-\sin \frac{4\pi}{9} \\\sin \frac{4\pi}{9}&\sin \frac {\pi}{18}\end{pmatrix}$. Then the smallest num...
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1 votes
1 answer
348
TIFR-2014-Maths-A-11
Let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$ (0-matrix), for some $k \in \mathbb{N}$. Then $A$ has to be the $0$ matrix Trace$(A)$ could be non-zero $A$ is diagonalizable $0$ is the only eigenvalue of $A$
Let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$ (0-matrix), for some $k \in \mathbb{N}$. Then$A$ has to be the $0$ matrix Trace$(A)$ could be non-...
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2 votes
1 answer
350
TIFR-2011-Maths-B-13
Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.
Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.
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2 votes
1 answer
351
TIFR-2011-Maths-B-8
If $A$ and $B$ are $3 \times 3$ matrices and $A$ is invertible, then there exists an integer $n$ such that $A + nB$ is invertible.
If $A$ and $B$ are $3 \times 3$ matrices and $A$ is invertible, then there exists an integer $n$ such that $A + nB$ is invertible.
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1 votes
0 answers
352
TIFR-2011-Maths-B-1
State True or False Let $A$ be a $2 \times 2$-matrix with complex entries. The number of $2 \times 2$-matrices $A$ with complex entries satisfying the equation $A^{3}$ is infinite.
State True or FalseLet $A$ be a $2 \times 2$-matrix with complex entries. The number of $2 \times 2$-matrices $A$ with complex entries satisfying the equation $A^{3}$ is ...
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4 votes
1 answer
353
TIFR-2011-Maths-A-3
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ has An eigenvalue which is purely imaginary At least one real eigenvalue At least two eigenvalues which are not real At least $2$ distinct real eigenvalues
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ hasAn eigenvalue which is purely imaginaryAt least one real eigenvalueAt least two eigenvalues which are not ...
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24 votes
3 answers
355
TIFR CSE 2013 | Part B | Question: 3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant?Hint: Use modulo $2$ arithmetic.$20160$$32767$$49152$$57343$$65520$
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22 votes
2 answers
356
TIFR CSE 2012 | Part B | Question: 12
Let $A$ be a matrix such that $A^{k}=0$. What is the inverse of $I - A$? $0$ $I$ $A$ $1 + A + A^{2} + ...+ A^{k - 1}$ Inverse is not guaranteed to exist.
Let $A$ be a matrix such that $A^{k}=0$. What is the inverse of $I - A$?$0$$I$$A$$1 + A + A^{2} + ...+ A^{k - 1}$Inverse is not guaranteed to exist.
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3 votes
1 answer
358
symmetric matrix
Let $A =\begin{bmatrix} P & Q\\ R & Q\ \end{bmatrix}$. If $P,Q,R$ and $S$ are symmetric , What can you say about $A$?
Let $A =\begin{bmatrix} P & Q\\ R & Q\ \end{bmatrix}$. If $P,Q,R$ and $S$ are symmetric , What can you say about $A$?
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3 votes
1 answer
360
TIFR2010-Maths-B-10
Let $x$ and $y \in \mathbb{R}^{n}$ be non-zero column vectors, from the matrix $A=xy^{T}$, where $y^{T}$ is the transpose of $y$. Then the rank of $A$ is: $2$ $0$ At least $n/2$ None of the above
Let $x$ and $y \in \mathbb{R}^{n}$ be non-zero column vectors, from the matrix $A=xy^{T}$, where $y^{T}$ is the transpose of $y$. Then the rank of $A$ is:$2$$0$At least $...
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