The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
ISI2018MMA13
0
votes
77
views
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is
$2$
$2(1+i)$
$0$
$2^{10}$
isi2018mma
engineeringmathematics
linearalgebra
determinant
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
41.8k
points)

77
views
answer
comment
Please
log in
or
register
to add a comment.
Please
log in
or
register
to answer this question.
2
Answers
+2
votes
$\begin{vmatrix} 2\lambda & i\\ i& \lambda \end{vmatrix}$=0
$(2\lambda)*\lambda+1=0$
$(\lambda1)^2=0$
$\lambda=1,1$
Eigen values of A is 1,1
Eigen values of $A^{10}$ will be $1^{10}, 1^{10}$=1,1
Trace of $A^{10}$=Sum of Eigen values=1+1=2
answered
Sep 23
by
aditi19
Active
(
5k
points)
comment
Please
log in
or
register
to add a comment.
+1
vote
By matrix multiplication , $A^2$ = $\begin{bmatrix} 3 &2i \\ 2i & 1 \end{bmatrix}$ whose trace is 2.
$A^3$ = $\begin{bmatrix} 4 & 3i\\ 3i & 2 \end{bmatrix}$ whose trace is 2.
So we see the trace of the original matrix remains the same irrespective of repeated multiplication with itself. Therefore trace of $A^{10}$ = 2
answered
May 12
by
Sayan Bose
Loyal
(
7.2k
points)
comment
Please
log in
or
register
to add a comment.
← Prev. Qn. in Sub.
Next Qn. in Sub. →
← Prev.
Next →
Related questions
0
votes
1
answer
1
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 $4$ $2$ $2$ $4$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
41.8k
points)

77
views
isi2018mma
engineeringmathematics
linearalgebra
eigenvalue
determinant
+2
votes
3
answers
2
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
41.8k
points)

113
views
isi2018mma
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
3
ISI2018MMA11
The value of $\lambda$ for which the system of linear equations $2xyz=12$, $x2y+z=4$ and $x+y+\lambda z=4$ has no solution is $2$ $2$ $3$ $3$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.8k
points)

73
views
isi2018mma
engineeringmathematics
linearalgebra
systemofequations
0
votes
0
answers
4
ISI2017MMA19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3px+q=0$, then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$
asked
Sep 15, 2018
in
Linear Algebra
by
jothee
Veteran
(
104k
points)

21
views
isi2017mma
engineeringmathematics
linearalgebra
determinant
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
OFFICIAL GATE MOCK TEST RELEASED
IIITH: Winter Research Admissions 2019 (For Spring 2020)
TIFR and JEST exam
Minimal Deterministic Finite Automata
To be aware of fake GATE test series
All categories
General Aptitude
1.9k
Engineering Mathematics
7.5k
Discrete Mathematics
5.2k
Probability
1k
Linear Algebra
722
Calculus
592
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.3k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.5k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.1k
Non GATE
1.5k
Others
1.5k
Admissions
595
Exam Queries
576
Tier 1 Placement Questions
23
Job Queries
72
Projects
17
Follow @csegate
Recent Blog Comments
These two subjects are very important for the...
Please anyone can provide me engineering...
No.....it means your application accepted i.e...
It says: "Candidates who meet the eligibility...
@ankitgupta.1729 Thanks a lot ... :)
50,650
questions
56,242
answers
194,294
comments
95,945
users