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Recent questions and answers in Linear Algebra
+1
vote
1
answer
1
ISI2018PCBA1
Consider a $n \times n$ matrix $A=I_n\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
answered
May 20
in
Linear Algebra
by
Kaustubh Vande
(
11
points)

30
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isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
1
answer
2
#GATE 2014 IN
answered
May 14
in
Linear Algebra
by
Satbir
Loyal
(
7.5k
points)

22
views
0
votes
1
answer
3
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
May 12
in
Linear Algebra
by
Sayan Bose
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6.9k
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27
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isi2018
engineeringmathematics
linearalgebra
determinant
0
votes
2
answers
4
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
May 11
in
Linear Algebra
by
srestha
Veteran
(
114k
points)

49
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isi2018
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
5
ISI2018MMA14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $4$ $2$ $2$ $4$
answered
May 11
in
Linear Algebra
by
Verma Ashish
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7k
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38
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isi2018
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
2
answers
6
ISI2019MMA13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$
answered
May 9
in
Linear Algebra
by
pratekag
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2k
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155
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isi2019
engineeringmathematics
linearalgebra
0
votes
1
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7
ISI2019MMA23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skewsymmetric matrix None of the above must necessarily hold
answered
May 7
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Linear Algebra
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pratekag
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100
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isi2019
engineeringmathematics
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0
votes
2
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8
ISI2019MMA15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & 1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
answered
May 7
in
Linear Algebra
by
Shikha Mallick
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3.5k
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136
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isi2019
linearalgebra
engineeringmathematics
0
votes
1
answer
9
ISI2019MMA14
If the system of equations $\begin{array} ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1a} + \frac{1}{1b} + \frac{1}{1c}$ is $1$ $1$ $3$ $3$
answered
May 7
in
Linear Algebra
by
MRINMOY_HALDER
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1.1k
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98
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isi2019
linearalgebra
systemofequations
+10
votes
4
answers
10
GATE199610
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two matrices such that $AB=I$. Let $C = A \begin{bmatrix} 1 && 0 \\ 1 && 1 \end{bmatrix}$ and $CD =I$. Express the elements of $D$ in terms of the elements of $B$.
answered
May 3
in
Linear Algebra
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MRINMOY_HALDER
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1.1k
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624
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gate1996
linearalgebra
matrices
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0
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0
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11
CSIR UGC NET
asked
Apr 28
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Linear Algebra
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Hirak
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2k
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33
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liner
linearalgebra
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matrixinversion
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0
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0
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12
Made Easy Engineering Maths book
The ans given is b, but i am not able to understande why. According to me the largest eigen value is 2, and therefore none of the option matches..!
asked
Apr 27
in
Linear Algebra
by
Hirak
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(
2k
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47
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+1
vote
2
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13
Virtual Gate Test Series: Linear Algebra  Rank Of The Matrix
answered
Apr 27
in
Linear Algebra
by
SuvasishDutta
Junior
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655
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58
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engineeringmathematics
linearalgebra
matrix
rankofmatrix
virtualgatetestseries
+2
votes
1
answer
14
Vani Institute Question Bank Pg231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $a,2a,2a$ $a,a+\sqrt{2},a\sqrt{2}$
answered
Apr 27
in
Linear Algebra
by
SuvasishDutta
Junior
(
655
points)

71
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engineeringmathematics
linearalgebra
eigenvalue
+3
votes
4
answers
15
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
Apr 23
in
Linear Algebra
by
gaurav1.yuva
(
403
points)

1.7k
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gate2019
engineeringmathematics
linearalgebra
determinant
+2
votes
1
answer
16
TIFR2015MathsB13
Let $X=\left\{(x, y) \in \mathbb{R}^{2}: 2x^{2}+3y^{2}= 1\right\}$. Endow $\mathbb{R}^{2}$ with the discrete topology, and $X$ with the subspace topology. Then. $X$ is a compact subset of $\mathbb{R}^{2}$ in this topology. $X$ is a connected subset of $\mathbb{R}^{2}$ in this topology. $X$ is an open subset of $\mathbb{R}^{2}$ in this topology. None of the above.
answered
Apr 8
in
Linear Algebra
by
Sushantkala786
(
11
points)

76
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tifrmaths2015
linearalgebra
0
votes
4
answers
17
ISRO 2012 ECE Matrices
The Eigen values of matrix are: a) ± cos∝ b) ± sin ∝ c) tan ∝ & cot ∝ d) cos ∝ ± sin ∝
answered
Mar 10
in
Linear Algebra
by
Debdeep1998
Junior
(
635
points)

101
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engineeringmathematics
isroece
isro2012ece
linearalgebra
eigenvalue
0
votes
3
answers
18
ISRO2012ECE: Engineering Mathematics
The system of equations x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8 has a. A unique solution b. No solution c. An infinite number of solutions d. None of these
answered
Mar 10
in
Linear Algebra
by
abhishekmehta4u
Boss
(
33.6k
points)

64
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isro2012ece
isroece
engineeringmathematics
linearalgebra
+3
votes
4
answers
19
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
answered
Mar 10
in
Linear Algebra
by
Verma Ashish
Loyal
(
7k
points)

210
views
matrices
eigenvalue
0
votes
1
answer
20
Ace Test Series: Linear Algebra  Eigen Values
answered
Mar 9
in
Linear Algebra
by
abhishekmehta4u
Boss
(
33.6k
points)

151
views
engineeringmathematics
linearalgebra
eigenvalue
0
votes
2
answers
21
ISRO 2014 Trigonometry [EE]
If tan $\Theta$ = 8 / 15 and $\Theta$ is acute, then cosec $\Theta$ (A) 8 / 17 (B) 8 / 15 (C) 17 / 8 (D) 17 / 15
answered
Mar 7
in
Linear Algebra
by
abhishekmehta4u
Boss
(
33.6k
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210
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isroee
engineeringmathematics
0
votes
0
answers
22
ISIMMA201544
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ It is given ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane
asked
Feb 22
in
Linear Algebra
by
ankitgupta.1729
Boss
(
11.3k
points)

76
views
engineeringmathematics
linearalgebra
userisi2015
usermod
0
votes
1
answer
23
Linear AlgebraMETest
If the determinant of the below matrix is 245, what is the value of X? $\begin{bmatrix} 0 & 4& 2 &1 \\ 3& 1 & 0 & 2\\ 5&2 & x& 4\\ 6& 1 & 1 & 0 \end{bmatrix}$ ... , because by keeping 6 in place of x I am getting determinant as 245(Result verified by computer program). Please let me know where I am going wrong?
answered
Feb 19
in
Linear Algebra
by
Meet2698
(
159
points)

138
views
linearalgebra
engineeringmathematics
+20
votes
4
answers
24
GATE2015227
Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.
answered
Feb 18
in
Linear Algebra
by
Ram Swaroop
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2.6k
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1.8k
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gate20152
linearalgebra
matrices
easy
numericalanswers
+14
votes
3
answers
25
GATE19982.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$ $3$ $1$ $2$ $4$
answered
Feb 18
in
Linear Algebra
by
Ram Swaroop
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2.6k
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1.6k
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gate1998
linearalgebra
matrices
normal
+4
votes
3
answers
26
ISRODEC201717
If $C$ is a skewsymmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is a scalar matrix null matrix unit matrix matrix will all elements $1$
answered
Feb 12
in
Linear Algebra
by
Abhisek Tiwari 4
Active
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4.7k
points)

1.4k
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isrodec2017
matrices
+3
votes
3
answers
27
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
Feb 7
in
Linear Algebra
by
Lakshman Patel RJIT
Boss
(
36.3k
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2.2k
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gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+21
votes
2
answers
28
GATE2015118
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
answered
Feb 6
in
Linear Algebra
by
Verma Ashish
Loyal
(
7k
points)

2.6k
views
gate20151
linearalgebra
matrices
numericalanswers
0
votes
0
answers
29
Previous gate
asked
Jan 31
in
Linear Algebra
by
Hemanth_13
Loyal
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6.6k
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75
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eigenvalue
0
votes
0
answers
30
#math
asked
Jan 30
in
Linear Algebra
by
amit166
Junior
(
761
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29
views
engineeringmathematics
0
votes
0
answers
31
ace test series
how? please explain
asked
Jan 28
in
Linear Algebra
by
Vignaneswarkrishna
(
187
points)

45
views
0
votes
1
answer
32
Gatebook Test
answered
Jan 28
in
Linear Algebra
by
Meet2698
(
159
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61
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0
votes
1
answer
33
Ace Test Series 2019: Discrete Maths  Recurrence Relation
answered
Jan 27
in
Linear Algebra
by
Meet2698
(
159
points)

77
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acetestseries
discretemathematics
recurrenceeqation
0
votes
0
answers
34
Gate 2016 ee
Question number 249
asked
Jan 27
in
Linear Algebra
by
Vignaneswarkrishna
(
187
points)

39
views
+14
votes
3
answers
35
GATE2004IT36
If matrix $X = \begin{bmatrix} a & 1 \\ a^2+a1 & 1a \end{bmatrix}$ and $X^2  X + I = O$ ($I$ is the identity matrix and $O$ is the zero matrix), then the inverse of $X$ is $\begin{bmatrix} 1a &1 \\ a^2& a \end{bmatrix}$ ... $\begin{bmatrix} a &1 \\ a^2+a1& 1a \end{bmatrix}$ $\begin{bmatrix} a^2a+1 &a \\ 1& 1a \end{bmatrix}$
answered
Jan 27
in
Linear Algebra
by
dsomnath
(
69
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901
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gate2004it
linearalgebra
matrices
normal
+31
votes
6
answers
36
GATE2007IT2
Let A be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of xT Ax where the maximum is taken over all x that are the unit eigenvectors of A? $3$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5  √5)}{2}$
answered
Jan 26
in
Linear Algebra
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Sambhrant Maurya
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1.7k
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3k
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gate2007it
linearalgebra
eigenvalue
normal
+1
vote
1
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37
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix By how to calculate value of x when nullity is already given(1 in this case)
answered
Jan 24
in
Linear Algebra
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Somoshree Datta 5
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116
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–1
vote
0
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38
acetest series
asked
Jan 21
in
Linear Algebra
by
Rajesh Panwar
Junior
(
605
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57
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0
votes
1
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39
Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,1. If $B=A^2A$ then B=? a)24 b)2 c)12 d)12 Please explain in detail.
answered
Jan 20
in
Linear Algebra
by
Rishabh Agrawal
Junior
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953
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92
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linearalgebra
matrix
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0
votes
1
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40
Simple Determinant
how to prove determinant 1 and 2 are same by some rowcolumn manipulation ,please Help??
answered
Jan 20
in
Linear Algebra
by
Rishabh Agrawal
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953
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51
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