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Recent questions and answers in Linear Algebra
+3
votes
4
answers
1
ISRO200834
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ is Idempotent Symmetric Orthogonal Hermitian
answered
3 days
ago
in
Linear Algebra
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JashanArora
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isro2008
linearalgebra
matrices
+4
votes
3
answers
2
GATE201944
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
answered
5 days
ago
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Linear Algebra
by
JashanArora
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1.8k
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2.7k
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gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+3
votes
5
answers
3
GATE20199
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is nonzero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
answered
6 days
ago
in
Linear Algebra
by
JashanArora
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1.8k
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2k
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gate2019
engineeringmathematics
linearalgebra
determinant
+7
votes
2
answers
4
GATE19952.13
A unit vector perpendicular to both the vectors $a=2i3j+k$ and $b=i+j2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+jk)$ $\frac{1}{3} (ijk)$ $\frac{1}{\sqrt{3}} (i+jk)$
answered
Nov 28
in
Linear Algebra
by
Satbir
Boss
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21.5k
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1.1k
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gate1995
linearalgebra
normal
vectorspace
0
votes
1
answer
5
ISI2015MMA44
Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by $\begin{array} {} a_1x +b_1y+c_1z=\alpha _1 \\ a_2x +b_2y+c_2z=\alpha _2 \\ a_3x +b_3y+c_3z=\alpha _3 \end{array}$ It is given that $P_1$, $P_2$ and $P_3$ ... then the planes do not have any common point of intersection intersect at a unique point intersect along a straight line intersect along a plane
answered
Nov 25
in
Linear Algebra
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Lakshman Patel RJIT
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14
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isi2015mma
linearalgebra
systemofequations
+2
votes
2
answers
6
ISI2015MMA39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
answered
Nov 25
in
Linear Algebra
by
Lakshman Patel RJIT
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32
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isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
7
ISI2014DCG64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & 4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $3$
answered
Nov 24
in
Linear Algebra
by
Lakshman Patel RJIT
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54.7k
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31
views
isi2014dcg
linearalgebra
matrices
systemofequations
+1
vote
1
answer
8
ISI2016DCG31
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ stands for determinant of matrix $A.$ Then $\mid\:(A)\mid=1$ $\mid\:(A)\mid=0\:\text{or}\:1$ $\mid\:(A)\mid=1,0\:\text{or}\:1$ $\mid\:(A)\mid=1\:\text{or}\:1$
answered
Nov 18
in
Linear Algebra
by
Lakshman Patel RJIT
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54.7k
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9
views
isi2016dcg
linearalgebra
matrices
determinant
+4
votes
3
answers
9
ISRO200709
Eigen vectors of $\begin{bmatrix} 1 && \cos \theta \\ \cos \theta && 1 \end{bmatrix}$ are $\begin{bmatrix} a^n && 1 \\ 0 && a^n \end{bmatrix}$ $\begin{bmatrix} a^n && n \\ 0 && a^n \end{bmatrix}$ ... $\begin{bmatrix} a^n && na^{n1} \\ n && a^n \end{bmatrix}$
answered
Nov 16
in
Linear Algebra
by
Viplove04
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17
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2.3k
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isro2007
linearalgebra
matrices
eigenvalue
+4
votes
5
answers
10
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
answered
Nov 12
in
Linear Algebra
by
JashanArora
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1.8k
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291
views
matrices
eigenvalue
+1
vote
3
answers
11
ISI2014DCG8
If $M$ is a $3 \times 3$ matrix such that $\begin{bmatrix} 0 & 1 & 2 \end{bmatrix}M=\begin{bmatrix}1 & 0 & 0 \end{bmatrix}$ and $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
answered
Nov 11
in
Linear Algebra
by
techbd123
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3.1k
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67
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isi2014dcg
linearalgebra
matrix
+4
votes
2
answers
12
TIFR2018A14
Let $A$ be an $n\times n$ invertible matrix with real entries whose row sums are all equal to $c$. Consider the following statements: Every row in the matrix $2A$ sums to $2c$. Every row in the matrix $A^{2}$ sums to $c^{2}$. Every row in the matrix $A^{1}$ ... $(1)$ and $(2)$ are correct but not necessarily statement $(3)$ all the three statements $(1), (2),$ and $(3)$ are correct
answered
Nov 9
in
Linear Algebra
by
rohith1001
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491
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tifr2018
matrices
linearalgebra
+14
votes
2
answers
13
TIFR2013B3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
answered
Nov 9
in
Linear Algebra
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rohith1001
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1.1k
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tifr2013
linearalgebra
matrices
+19
votes
4
answers
14
GATE201211
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
answered
Oct 31
in
Linear Algebra
by
Praveenk99
(
49
points)

2.6k
views
gate2012
linearalgebra
eigenvalue
+21
votes
5
answers
15
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? $p  q + r = 0 \text{ or } p = q = r$ $p + q  r = 0 \text{ or } p = q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p  q + r = 0 \text{ or } p = q = r$
answered
Oct 30
in
Linear Algebra
by
techbd123
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3.1k
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2.9k
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gate20153
linearalgebra
systemofequations
normal
+23
votes
6
answers
16
GATE2017252
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______
answered
Oct 28
in
Linear Algebra
by
techbd123
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3.1k
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3.8k
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gate20172
engineeringmathematics
linearalgebra
numericalanswers
eigenvalue
+18
votes
2
answers
17
GATE19974.2
Let $A=(a_{ij})$ be an $n$rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$rowed Identify matrix. Then $AI_{12}$ is such that its first Row is the same as its second row Row is the same as the second row of $A$ Column is the same as the second column of $A$ Row is all zero
answered
Oct 24
in
Linear Algebra
by
Satbir
Boss
(
21.5k
points)

1k
views
gate1997
linearalgebra
easy
matrices
+21
votes
2
answers
18
GATE2017222
Let $P = \begin{bmatrix}1 & 1 & 1 \\2 & 3 & 4 \\3 & 2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}1 & 2 &1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .
answered
Oct 24
in
Linear Algebra
by
Satbir
Boss
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21.5k
points)

2.9k
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gate20172
linearalgebra
eigenvalue
numericalanswers
+8
votes
3
answers
19
GATE200549
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & 1\\ 4 & 5\end{array}\right)$ $1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $1$
answered
Oct 23
in
Linear Algebra
by
Satbir
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21.5k
points)

866
views
gate2005
linearalgebra
eigenvalue
easy
+1
vote
1
answer
20
Gatebook Test
answered
Oct 22
in
Linear Algebra
by
aditi19
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5.1k
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50
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0
votes
1
answer
21
Gatebook Test
answered
Oct 22
in
Linear Algebra
by
aditi19
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5.1k
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48
views
0
votes
1
answer
22
ISI2015MMA61
Let $ A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{pmatrix} \text{ and } B=\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{pmatrix}.$ Then there exists a matrix $C$ ... no matrix $C$ such that $A=BC$ there exists a matrix $C$ such that $A=BC$, but $A \neq CB$ there is no matrix $C$ such that $A=CB$
answered
Oct 19
in
Linear Algebra
by
chirudeepnamini
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3.1k
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15
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
23
ISI2015MMA43
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta = 1, 2$ $\eta = 1, 2$ $\eta = 3, 3$ $\eta = 1, 2$
answered
Oct 19
in
Linear Algebra
by
chirudeepnamini
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3.1k
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14
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isi2015mma
linearalgebra
systemofequations
+9
votes
5
answers
24
GATE2007IT80
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the ... largest or the smallest $y$coordinate among all the points The difference between $x$coordinates $P_{a}$ and $P_{b}$ is minimum None of the above
answered
Oct 4
in
Linear Algebra
by
sujeetkumar
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15
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1.1k
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gate2007it
cartesiancoordinates
+1
vote
1
answer
25
ISI2014DCG9
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta=1, 2$ $\eta=1, 2$ $\eta=3, 3$ $\eta=1, 2$
answered
Sep 29
in
Linear Algebra
by
techbd123
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3.1k
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36
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isi2014dcg
linearalgebra
systemofequations
0
votes
1
answer
26
ISI2015MMA63
Let $\theta=2\pi/67$. Now consider the matrix $A = \begin{pmatrix} \cos \theta & \sin \theta \\  \sin \theta & \cos \theta \end{pmatrix}$. Then the matrix $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
answered
Sep 25
in
Linear Algebra
by
`JEET
Boss
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13.1k
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11
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isi2015mma
linearalgebra
matrices
trigonometry
0
votes
1
answer
27
ISI2015MMA62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
answered
Sep 25
in
Linear Algebra
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Verma Ashish
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11.8k
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23
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isi2015mma
linearalgebra
matrices
eigenvalue
+1
vote
1
answer
28
ISI2014DCG25
The determinant $\begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix}$ equals $\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ ... $3\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ None of these
answered
Sep 24
in
Linear Algebra
by
`JEET
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13.1k
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36
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isi2014dcg
linearalgebra
determinant
+1
vote
0
answers
29
ISI2014DCG38
Suppose that $A$ is a $3 \times 3$ real matrix such that for each $u=(u_1, u_2, u_3)’ \in \mathbb{R}^3, \: u’Au=0$ where $u’$ stands for the transpose of $u$. Then which one of the following is true? $A’=A$ $A’=A$ $AA’=I$ None of these
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Sep 23
in
Linear Algebra
by
Arjun
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424k
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19
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isi2014dcg
linearalgebra
matrices
realmatrix
0
votes
0
answers
30
ISI2014DCG70
For the matrices $A = \begin{pmatrix} a & a \\ 0 & a \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$, $(B^{1}AB)^3$ is equal to $\begin{pmatrix} a^3 & a^3 \\ 0 & a^3 \end{pmatrix}$ ... $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$ $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$
asked
Sep 23
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Linear Algebra
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Arjun
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424k
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18
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isi2014dcg
linearalgebra
matrices
inverse
0
votes
0
answers
31
ISI2015MMA37
Let $a$ be a nonzero real number. Define $f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is $1$ $2$ $3$ $4$
asked
Sep 23
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Linear Algebra
by
Arjun
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424k
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21
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isi2015mma
linearalgebra
determinant
functions
0
votes
0
answers
32
ISI2015MMA38
A real $2 \times 2$ matrix $M$ such that $M^2 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \varepsilon \end{pmatrix}$ exists for all $\varepsilon > 0$ does not exist for any $\varepsilon > 0$ exists for some $\varepsilon > 0$ none of the above is true
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
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424k
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9
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isi2015mma
linearalgebra
matrices
0
votes
0
answers
33
ISI2015MMA40
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define a $4 \times 4$ matrix $\textbf{A}$ ... $(\textbf{A})$ equals $1$ or $2$ $0$ $4$ $2$ or $3$
asked
Sep 23
in
Linear Algebra
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Arjun
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424k
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19
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isi2015mma
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
34
ISI2015MMA42
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 &  \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{  \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{  \frac{\pi}{3}, \frac{\pi}{3} \}$
asked
Sep 23
in
Linear Algebra
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Arjun
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18
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isi2015mma
linearalgebra
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eigenvalue
+2
votes
3
answers
35
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
answered
Sep 23
in
Linear Algebra
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aditi19
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isi2018mma
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
2
answers
36
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
answered
Sep 23
in
Linear Algebra
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aditi19
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isi2018mma
engineeringmathematics
linearalgebra
determinant
0
votes
1
answer
37
ISI2015DCG32
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is $\begin{Bmatrix} \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these
answered
Sep 23
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Linear Algebra
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Sourajit25
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44
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isi2015dcg
linearalgebra
matrices
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+1
vote
1
answer
38
ISI2016DCG22
The value of $\:\:\begin{vmatrix} 1&\log_{x}y &\log_{x}z \\ \log_{y}x &1 &\log_{y}z \\\log_{z}x & \log_{z}y&1 \end{vmatrix}\:\:$ is $0$ $1$ $1$ None of these
answered
Sep 22
in
Linear Algebra
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`JEET
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13.1k
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15
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isi2016dcg
linearalgebra
determinant
0
votes
1
answer
39
ISI2017DCG4
If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +AI= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is $A$ $O$ $I$ none of these
answered
Sep 21
in
Linear Algebra
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kp1
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115
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11
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isi2017dcg
linearalgebra
matrices
nullmatrix
identitymatrix
0
votes
1
answer
40
ISI2015DCG34
Let $A_{ij}$ denote the minors of an $n \times n$ matrix $A$. What is the relationship between $\mid A_{ij} \mid $ and $\mid A_{ji} \mid $? They are always equal $\mid A_{ij} \mid = – \mid A _{ji} \mid \text{ if } i \neq j$ They are equal if $A$ is a symmetric matrix If $\mid A_{ij} \mid =0$ then $\mid A_{ji} \mid =0$
answered
Sep 21
in
Linear Algebra
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Satbir
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12
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isi2015dcg
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