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Gate 2015 CE set 2
The two eigen values of the matrix $\begin{bmatrix} 2 & 1\\ 1& p \end{bmatrix}$ have a ratio of 3:1 for p= 2. What is another value of p for which eigenvalues have the same ratio of 3:1? A)2 b) 1 c) 7/3 d)14/3
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Eigen vector
Is it true that if we have 3 distinct eigen vectors x,y and z than x,y and z would respectively be orthogonal to each other .Please elaborate
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Gate 2016 ME Set 2
The condition for which the eigen values of the matrix A = $\begin{pmatrix} 2 &1 \\ 1& k \end{pmatrix}$ are positive, is a) k>1/2 b) k>2 c) k>0 d) k< 1/2
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Gate 2016 CE Set 1
If the entries in each column of a square matrix M add up to 1, then an eigen value of M is A) 4 B) 3 C) 2 D) 1
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made easy ME previou year question
which on of the following is an eigenvector of the matrix [5 0 0 0 0 5 5 0 0 0 2 1 0 0 3 1] a) [1 2 0 0 ]t b) [0 0 1 0]t c) [1 0 0 2]t d) [1 1 2 1]t
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Gate2016
A 3×3 matrix p is such that,p^3=p. Then eigen values of p are
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GATE2015333
If the following system has nontrivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p  q + r = 0 \text{ or } p = q = r$ $p + q  r = 0 \text{ or } p = q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p  q + r = 0 \text{ or } p = q = r$
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gate 2014
Two matrices A and B are given below: A= p q r s B= p2 + q2 pr + qs pr +qs r2 + s2 If the rank of matrix A is N, then the rank of matrix B is (A) N /2 (B) N1 (C) N (D) 2 N
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Aug 10
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Engineering mathematics
if the sum of the diagonal elements of a 2x2 matrix is (6) then the maximum possible value of determinant of the matrix is
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Engineering Mathematics  Linear Algebra
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Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.
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Invertible Matrix
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{1}$.
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TIFR2015MathsA1
Let $A$ be an invertible $10 \times 10$ matrix with real entries such that the sum of each row is $1$. Then The sum of the entries of each row of the inverse of $A$ is $1$. The sum of the entries of each column of the inverse of $A$ is $1$. The trace of the inverse of $A$ is nonzero. None of the above.
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+6
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3
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15
GATE19871xxi
If $a, b,$ and $c$ are constants, which of the following is a linear inequality? $ax+bcy=0$ $ax^{2}+cy^{2}=21$ $abx+a^{2}y \geq 15$ $xy+ax \geq 20$
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Aug 8
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gate1987
linearalgebra
inequality
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16
#idempotent #matrix
If Matrix A and B are of same size and AB=B and BA=A. Then the value of $(A+B)^{5}$ is _____________?
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Aug 8
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17
GATE2017131
Let $A$ be $n\times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} =$ 50. Consider the following statements. One eigenvalue must be in $\left [ 5,5 \right ]$ The eigenvalue with the largest ... greater than 5 Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
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Jul 20
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Gyanu
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gate20171
linearalgebra
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+7
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3
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18
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
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Jul 16
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Ayush Upadhyaya
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isi2016
matrices
+19
votes
3
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19
GATE19961.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and only if, both $A$ ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.
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Jul 15
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gate1996
linearalgebra
systemofequations
normal
+16
votes
5
answers
20
GATE201414
Consider the following system of equations: $3x + 2y = 1 $ $4x + 7z = 1 $ $x + y + z = 3$ $x  2y + 7z = 0$ The number of solutions for this system is ______________
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Jul 15
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gate20141
linearalgebra
systemofequations
numericalanswers
normal
+21
votes
4
answers
21
GATE201713
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ where $A=\left [ a_{1}.....a_{n} \ ... of equations has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
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Jul 15
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Ayush Upadhyaya
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3.3k
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gate20171
linearalgebra
systemofequations
normal
+18
votes
3
answers
22
GATE2008IT29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the ... : $MX = 0$ has a nontrivial solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$
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Jul 15
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gate2008it
linearalgebra
normal
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+13
votes
2
answers
23
GATE199301.1
In questions $1.1$ to $1.7$ below, one or more of the alternatives are correct. Write the code letter$(s)$ $a$, $b$, $c$, $d$ corresponding to the correct alternative$(s) $ in the answer book. Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is ... },\alpha \neq 0$$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
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Jul 14
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Ayush Upadhyaya
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11.1k
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1.1k
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gate1993
eigenvalue
linearalgebra
easy
+32
votes
6
answers
24
GATE2014247
The product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
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Jul 14
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gate20142
linearalgebra
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0
votes
0
answers
25
Kenneth Rosen 2.1
Determine True or False $a)x\varepsilon \left \{ x \right \}$ $b)\left \{ x \right \}\subseteq \left \{ x \right \}$ $c)\left \{ x \right \}\varepsilon \left \{ x \right \}$
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Jul 13
in
Linear Algebra
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srestha
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92.2k
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37
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settheory&algebra
discretemathematics
+15
votes
5
answers
26
GATE2015315
In the given matrix $\begin{bmatrix} 1 & 1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 are $\left\{a\left(4,2,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$ $\ ... \neq 0, a \in \mathbb{R}\right\}$ $\left\{a\left( \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$
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Jul 13
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Ayush Upadhyaya
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1.7k
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gate20153
linearalgebra
eigenvalue
normal
+12
votes
2
answers
27
GATE 2013 ECA27
Let A be an mxn matrix and B an nxm matrix. It is given that determinant ( Im + AB ) = determinant ( In + BA ) , where Ik is the k×k identity matrix. Using the above property, the determinant of the matrix given below is $\begin{bmatrix} 2& 1& 1& 1\\ 1& 2& 1& 1\\ 1& 1& 2& 1\\ 1& 1& 1& 2 \end{bmatrix}$ A) 2 B) 5 C) 8 D) 16
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gate2013ec
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0
votes
1
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28
ugc net 2018 july10
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0
votes
0
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29
orthogonal matrix
Is the determinent of both the orthogonal and orthonormal is +1?for orthonormal im always getting +1 but for orthogonal its always +C,not 1,C=mag of the vector matrix
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Ankush Saha
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1
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30
Inversion of a matrix  CSIR question
Let A be 3x3 matrix. Suppose 1 and 1 are two of the three Eigen Values of A and 18 is one of the Eigen Values of A2+3A. Then____ a.) Both A and A2+3A are invertible. b.) A2+3A but A is not. c.) A is invertible but A2+3A is not invertible. d.) Both A and A2+3A are not invertible.
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Jul 5
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0
votes
3
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31
Made easy test
Consider the rank of matrix $'A'$ of size $(m \times n)$ is $"m1"$. Then, which of the following is true? $AA^T$ will be invertible. $A$ have $"m1"$ linearly independent rows and $"m1"$ linearly ... and $"n"$ linearly independent columns. $A$ will have $"m1"$ linearly independent rows and $"n1"$ independent columns.
answered
Jun 29
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141
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engineeringmathematics
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0
votes
2
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32
GATE 2018 Maths  44(Electrical Engineering)
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Jun 29
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gate2018
engineeringmathematics
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1
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33
Engineering Maths: Orthogonal Matrix
Is the given last point correct? But as i see in the given matrix sum of the product of first two columns (or) two rows is not zero. please verify.
answered
Jun 29
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Vinod Jaggavarapu
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17
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29
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linearalgebra
engineeringmathematics
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4
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34
ISI201604
If $a,b,c$ and $d$ satisfy the equations $$a+7b+3c+5d =16\\8a+4b+6c+2d = 16\\ 2a+6b+4c+8d = 16 \\ 5a+3b+7c+d= 16$$ Then $(a+d)(b+c)$ equals $4$ $0$ $16$ $16$
answered
Jun 28
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Navneet Kalra
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141
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122
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isi2016
engineeringmathematics
systemofequations
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1
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35
Test Series ACE
How to solve? ________________ Number of nonnegative integer solutions such that x+y+z=17 where x>1,y>2,z>3 is 
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Navneet Kalra
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141
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82
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systemofequations
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1
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36
GATE Linear Algebra
For what values of $\lambda$ the system of equations will have $2$ linear independent solutions  $x + y + z = 0$ $(\lambda + 1) y + (\lambda + 1) z = 0$ ($\lambda^{2} 1) z = 0$ Now the problem i'm facing is if there is ... rank of matrix will be $1$. Can anyone please explain in simple why the rank of matrix should be $1$ if we need $2$ Linear Independent solution. Thankyou.
answered
Jun 28
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Navneet Kalra
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141
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84
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numericalanswers
linear
algebra
system
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systemofequations
+11
votes
6
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37
GATE20011.1
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be nonsingular S2: The sum of two $n \times n$ nonsingular matrices may be singular Which one of the following statements is correct? $S1$ and $S2$ both are true $S1$ is true, $S2$ is false $S1$ is false, $S2$ is true $S1$ and $S2$ both are false
answered
Jun 23
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Prince Sindhiya
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1k
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gate2001
linearalgebra
normal
matrices
+14
votes
4
answers
38
GATE200426
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2  n\right)}{2}\right)$
answered
Jun 19
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janeb abhishek
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357
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2.3k
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gate2004
linearalgebra
normal
matrices
+20
votes
4
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39
GATE200623
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
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Jun 19
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janeb abhishek
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357
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gate2006
linearalgebra
normal
matrices
+1
vote
2
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40
mathematics
Consider the set H of all 3 × 3 matrices of the type where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is a group a monoid but not a group C a semigroup but not a monoid D neither a group nor a semigroup
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Jun 13
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