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Recent questions and answers in Linear Algebra
+3
votes
4
answers
1
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
1 day
ago
in
Linear Algebra
by
gaurav1.yuva
(
45
points)

1.6k
views
gate2019
engineeringmathematics
linearalgebra
determinant
+2
votes
1
answer
2
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)

72
views
tifrmaths2015
linearalgebra
0
votes
4
answers
3
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)

88
views
engineeringmathematics
isroece
isro2012ece
linearalgebra
eigenvalue
0
votes
3
answers
4
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
(
33.4k
points)

56
views
isro2012ece
isroece
engineeringmathematics
linearalgebra
+3
votes
4
answers
5
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
(
6.6k
points)

194
views
matrices
eigenvalue
0
votes
1
answer
6
Ace Test Series: Linear Algebra  Eigen Values
answered
Mar 9
in
Linear Algebra
by
abhishekmehta4u
Boss
(
33.4k
points)

135
views
engineeringmathematics
linearalgebra
eigenvalue
0
votes
2
answers
7
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
(
33.4k
points)

202
views
isroee
engineeringmathematics
0
votes
0
answers
8
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
(
10.7k
points)

60
views
engineeringmathematics
linearalgebra
userisi2015
usermod
0
votes
1
answer
9
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
(
151
points)

131
views
linearalgebra
engineeringmathematics
+20
votes
4
answers
10
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
Active
(
2.6k
points)

1.8k
views
gate20152
linearalgebra
matrices
easy
numericalanswers
+14
votes
3
answers
11
GATE19982.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &2 \end{bmatrix}$ $3$ $1$ $2$ $4$
answered
Feb 18
in
Linear Algebra
by
Ram Swaroop
Active
(
2.6k
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1.6k
views
gate1998
linearalgebra
matrices
normal
+4
votes
3
answers
12
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
(
4.4k
points)

1.4k
views
isrodec2017
matrices
+3
votes
3
answers
13
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
(
34.5k
points)

2.1k
views
gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+21
votes
2
answers
14
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
(
6.6k
points)

2.6k
views
gate20151
linearalgebra
matrices
numericalanswers
0
votes
0
answers
15
Previous gate
asked
Jan 31
in
Linear Algebra
by
Hemanth_13
Loyal
(
6.6k
points)

70
views
eigenvalue
0
votes
0
answers
16
#math
asked
Jan 30
in
Linear Algebra
by
amit166
Junior
(
761
points)

21
views
engineeringmathematics
0
votes
0
answers
17
ace test series
how? please explain
asked
Jan 28
in
Linear Algebra
by
Vignaneswarkrishna
(
187
points)

40
views
0
votes
1
answer
18
Gatebook Test
answered
Jan 28
in
Linear Algebra
by
Meet2698
(
151
points)

50
views
0
votes
1
answer
19
Ace Test Series 2019: Discrete Maths  Recurrence Relation
answered
Jan 27
in
Linear Algebra
by
Meet2698
(
151
points)

66
views
acetestseries
discretemathematics
recurrenceeqation
0
votes
0
answers
20
Gate 2016 ee
Question number 249
asked
Jan 27
in
Linear Algebra
by
Vignaneswarkrishna
(
187
points)

32
views
+14
votes
3
answers
21
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
points)

882
views
gate2004it
linearalgebra
matrices
normal
+31
votes
6
answers
22
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
by
Sambhrant Maurya
Active
(
1.7k
points)

2.9k
views
gate2007it
linearalgebra
eigenvalue
normal
+1
vote
1
answer
23
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
by
Somoshree Datta 5
Active
(
4.8k
points)

102
views
engineeringmathematics
linearalgebra
matrices
rankofmatrix
matrix
–1
vote
0
answers
24
acetest series
asked
Jan 21
in
Linear Algebra
by
Rajesh Panwar
Junior
(
601
points)

52
views
0
votes
1
answer
25
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
(
953
points)

83
views
linearalgebra
matrix
eigenvalue
0
votes
1
answer
26
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
Junior
(
953
points)

46
views
linearalgebra
engineeringmathematics
matrices
+16
votes
4
answers
27
GATE201826
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
answered
Jan 19
in
Linear Algebra
by
dnivara
(
37
points)

4.9k
views
gate2018
linearalgebra
matrices
eigenvalue
normal
0
votes
1
answer
28
MadeEasy Full Length Test 2019: Engineering Mathematics  Linear Algebra
answered
Jan 17
in
Linear Algebra
by
kd.....
Junior
(
883
points)

61
views
linearalgebra
engineeringmathematics
madeeasytestseries2019
madeeasytestseries
0
votes
0
answers
29
uppcl2018
need soln
[closed]
asked
Jan 11
in
Linear Algebra
by
SAUMYA2019
(
105
points)

22
views
0
votes
1
answer
30
GATEBOOK2019 Grand Test Mathematics10
Consider the system of equation $2x+3y+5z = 30 \\ 4x+6y+10z =40 \\ x+y z = 2 $ The above system has No solution a unique solution More than one but finite solutions an infinite number of solutions
answered
Jan 11
in
Linear Algebra
by
pranay562
Active
(
1.2k
points)

51
views
gb2019gtmaths
0
votes
0
answers
31
made easy
The probability of a man hitting a target in one fire is 1/4 The number of times at least he must fire at the target in order that his chance of hitting the target at least once will exceed 2/3 will be _______.
asked
Jan 7
in
Linear Algebra
by
pream sagar
Active
(
2.7k
points)

80
views
+1
vote
0
answers
32
made easy
If 2, – 4 are the eigen values of a nonsingular matrix A and A = –8, then the eigen values of Adj A are x and –y then the value of x + y is _________.
asked
Jan 7
in
Linear Algebra
by
pream sagar
Active
(
2.7k
points)

66
views
0
votes
0
answers
33
Doubt on syllabus
Is LU decomposition in course for GATE 2019?
[closed]
asked
Jan 6
in
Linear Algebra
by
subho16
(
189
points)

40
views
engineeringmathematics
ludecomposition
linearalgebra
0
votes
0
answers
34
GATE 2008 C.E.
The eigen values of the matrix [P] = 4 5 are? 2 5 The answer for this is 6 and 5. My question is what wrong am I doing by R1 = R1 + R2 and converting it to lower triangular matrix. Answer after this is +6 and 5 i.e. sign of eigen values inverted.
asked
Jan 6
in
Linear Algebra
by
Barney Ross
(
315
points)

37
views
0
votes
0
answers
35
UPPCL AE 2018:58
asked
Jan 5
in
Linear Algebra
by
Lakshman Patel RJIT
Boss
(
34.5k
points)

24
views
uppcl2018
+18
votes
2
answers
36
GATE201434
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. If the ... its eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
answered
Jan 5
in
Linear Algebra
by
Parth Shah
Junior
(
699
points)

2.1k
views
gate20143
linearalgebra
eigenvalue
normal
0
votes
0
answers
37
Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{1}$ ?
asked
Jan 4
in
Linear Algebra
by
Shamim Ahmed
Active
(
2.5k
points)

79
views
eigenvalue
engineeringmathematics
linearalgebra
0
votes
0
answers
38
Gatebook Test
[closed]
asked
Jan 4
in
Linear Algebra
by
Shadan Karim
Junior
(
977
points)

72
views
+1
vote
0
answers
39
Gatebook Test
asked
Jan 4
in
Linear Algebra
by
Shadan Karim
Junior
(
977
points)

76
views
0
votes
0
answers
40
Gatebook Test
asked
Jan 4
in
Linear Algebra
by
Shadan Karim
Junior
(
977
points)

34
views
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