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Recent questions tagged matrices
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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 $A^2=A$.
asked
May 12
in
Linear Algebra
by
akash.dinkar12
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40.6k
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33
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isi2018pcba
engineeringmathematics
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2
CSIR UGC NET
asked
Apr 28
in
Linear Algebra
by
Hirak
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2k
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33
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liner
linearalgebra
eigenvalue
matrixinversion
matrices
+1
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1
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3
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)
asked
Jan 24
in
Linear Algebra
by
Nandkishor3939
Active
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1.2k
points)

117
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engineeringmathematics
linearalgebra
matrices
rankofmatrix
matrix
0
votes
1
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4
Simple Determinant
how to prove determinant 1 and 2 are same by some rowcolumn manipulation ,please Help??
asked
Jan 19
in
Linear Algebra
by
BHASHKAR
(
31
points)

52
views
linearalgebra
engineeringmathematics
matrices
+1
vote
0
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5
#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup
asked
Jan 5
in
Set Theory & Algebra
by
Kunal Kadian
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2.6k
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59
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settheory&algebra
groups
matrices
0
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0
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6
Determinant
True and false IF A is 5*5 matrix then det(4$A^{3}$)=$4^{5}det(A^{3}))$ det($(4A)^{3}$)=$det(4^{3}A^{3}))$ i think both are true ??
asked
Jan 4
in
Mathematical Logic
by
Gurdeep Saini
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9.5k
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40
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engineeringmathematics
matrices
easy
+2
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1
answer
7
GATEBOOK2019LA11
The characteristic roots of a $3 \times 3$ matrix $A$ are $2, 2, 8.$ The constant term in the characteristic polynomial is $12$ $18$ $32$ $128$
asked
Dec 23, 2018
in
Linear Algebra
by
GATEBOOK
Boss
(
17.3k
points)

231
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gb2019la1
matrices
+2
votes
1
answer
8
Cases when LU decomposition is possible.
I had already visited below link but was unable to grasp it. https://math.stackexchange.com/questions/218770/whendoesasquarematrixhaveanludecomposition. I made some form of selfanalysis, let me know if I am in the correct ... pivot, and if such cannot be fixed without a row shuffle operation, then LU decomposition is not possible. Am I correct?
asked
Nov 18, 2018
in
Linear Algebra
by
Ayush Upadhyaya
Boss
(
25.4k
points)

193
views
linearalgebra
matrices
+1
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0
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9
Zeal Test Series 2019: Linear Algebra  Matrices
asked
Nov 17, 2018
in
Linear Algebra
by
Prince Sindhiya
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6.3k
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62
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zeal
linearalgebra
discretemathematics
matrices
zeal2019
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10
GATEME2016
asked
Nov 6, 2018
in
Linear Algebra
by
aditi19
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3.5k
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105
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gate20161
linearalgebra
matrices
eigenvalue
0
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0
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11
Virtual Gate Test Series: Linear Algebra  Eigen Value
asked
Oct 16, 2018
in
Linear Algebra
by
Prince Sindhiya
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6.3k
points)

44
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engineeringmathematics
linearalgebra
matrices
eigenvalue
virtualgatetestseries
0
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0
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12
Virtual Gate Test Series: Linear Algebra  Eigen Values of a Unity Matrix
asked
Oct 15, 2018
in
Linear Algebra
by
Prince Sindhiya
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6.3k
points)

62
views
engineeringmathematics
linearalgebra
matrices
eigenvalue
virtualgatetestseries
+3
votes
4
answers
13
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
asked
Sep 20, 2018
in
Linear Algebra
by
aditi19
Active
(
3.5k
points)

210
views
matrices
eigenvalue
0
votes
0
answers
14
ISI2017MMA5
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{1}$? $1$ $1/3$ $1/6$ $1/2$
asked
Sep 15, 2018
in
Linear Algebra
by
jothee
Veteran
(
116k
points)

31
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isi2017
engineeringmathematics
linearalgebra
matrices
0
votes
0
answers
15
ISI2017MMA15
The diagonal elements of a square matrix $M$ are odd integers while the offdiagonals are even integers. Then $M$ must be singular $M$ must be nonsingular there is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue
asked
Sep 15, 2018
in
Linear Algebra
by
jothee
Veteran
(
116k
points)

7
views
isi2017
engineeringmathematics
linearalgebra
matrices
0
votes
0
answers
16
ISI2017MMA20
The number of ordered pairs $(X, Y)$, where $X$ and $Y$ are $n \times n$ real, matrices such that $XYYX=I$ is $0$ $1$ $n$ infinite
asked
Sep 15, 2018
in
Linear Algebra
by
jothee
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116k
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7
views
isi2017
engineeringmathematics
linearalgebra
matrices
0
votes
0
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17
Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.
asked
Aug 8, 2018
in
Linear Algebra
by
pankaj_vir
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(
10.3k
points)

80
views
engineeringmathematics
linearalgebra
matrices
matrix
0
votes
2
answers
18
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 $A^{1}$.
asked
Aug 8, 2018
in
Linear Algebra
by
pankaj_vir
Boss
(
10.3k
points)

141
views
engineeringmathematics
linearalgebra
matrices
matrix
easy
0
votes
1
answer
19
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.
asked
Jul 5, 2018
in
Linear Algebra
by
ZeroFriction
(
15
points)

167
views
linearalgebra
matrices
engineeringmathematics
eigenvalue
matrixinversion
0
votes
3
answers
20
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 ... $"n"$ linearly independent columns. $A$ will have $"m1"$ linearly independent rows and $"n1"$ independent columns.
asked
May 31, 2018
in
Linear Algebra
by
saumya mishra
Active
(
1.5k
points)

184
views
engineeringmathematics
linearalgebra
matrices
+1
vote
1
answer
21
Matrix
Each row of M can be represented as a linear combination of the other rows 1)Does that mean linear combination of other rows will be 0? how ? 2)And also , is linear combination means add, subtract, multiply and divide , but not squaring or root or exponential operation,right? https://gateoverflow.in/3319/gate2008it29
asked
May 30, 2018
in
Linear Algebra
by
srestha
Veteran
(
114k
points)

144
views
linearalgebra
matrices
engineeringmathematics
+1
vote
3
answers
22
Matrix
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$ satisfies the following polynomial $A^{5}4A^{4}7A^{3}+11A^{2}2A+kI=0$ Then the value of k is ______________
asked
May 26, 2018
in
Linear Algebra
by
srestha
Veteran
(
114k
points)

478
views
linearalgebra
matrices
engineeringmathematics
0
votes
0
answers
23
Matrix
To find the product of the nonzero eigenvalues of the matrix is ____ ... $\lambda =1,2,0$ Where is my mistake, plz tell me
asked
May 14, 2018
in
Linear Algebra
by
srestha
Veteran
(
114k
points)

200
views
linearalgebra
matrices
engineeringmathematics
+2
votes
2
answers
24
ISI2017MMA15
The diagonal elements of a square matrix $M$ are odd integers while the offdiagonals are even integers. Then $M$ must be singular $M$ must be nonsingular There is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue.
asked
Mar 27, 2018
in
Linear Algebra
by
jjayantamahata
Active
(
1.8k
points)

191
views
isi2017
engineeringmathematics
linearalgebra
matrices
+3
votes
1
answer
25
Made easy workbook
Let $A$ be a $4\times 4$ matrix with real entries such that $1,1,2,2$ are eigen values.If $B=A^45A^2+5I$ then trace of $A+B$ is...........
asked
Mar 22, 2018
in
Linear Algebra
by
Avik Chowdhury
Junior
(
931
points)

271
views
matrices
eigenvalue
+3
votes
1
answer
26
Madeeasy workbook
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is $2\times 4^4$ $3\times 4^4$ $4\times 4^4$ $3\times 2^4$
asked
Mar 22, 2018
in
Linear Algebra
by
Avik Chowdhury
Junior
(
931
points)

132
views
matrices
+2
votes
2
answers
27
Madeeasy workbook
A $3\times 3$ matrix $P$ is such that $P^3 =P$.Then the eigenvalues of $P$ are $1,1,1$ $1,0.5+j(0.886),0.5j(0.866)$ $1,0.5+j(0.866),0.5j(0.886)$ $0,1,1$
asked
Mar 22, 2018
in
Linear Algebra
by
Avik Chowdhury
Junior
(
931
points)

157
views
matrices
eigenvalue
+1
vote
2
answers
28
Madeeasy workbook
Let $A$ be a $3\times 3$ matrix such that $\mid AI \mid=0$.If trace of $A=13$ and $det A = 32$ then sum of squares of the eigen values of $A$ is ..... $82$ $13$ $169$ $81$
asked
Mar 22, 2018
in
Linear Algebra
by
Avik Chowdhury
Junior
(
931
points)

638
views
matrices
eigenvalue
+2
votes
2
answers
29
Madeeasy workbook
Let $A$ be a $3\times 4$ matrix.The system of equations $Ax=0$ has unique solution Infinite solution No solution Exactly 2 solutions
asked
Mar 22, 2018
in
Linear Algebra
by
Avik Chowdhury
Junior
(
931
points)

2.2k
views
matrices
+1
vote
1
answer
30
Made easy workbook
Let $A = (a_{ij})_{n\times n}$ such that $a_{ij}=3$ for all $i,j$ then nullity of $A$ is $n1$ $n3$ $n$ $0$
asked
Mar 22, 2018
in
Linear Algebra
by
Avik Chowdhury
Junior
(
931
points)

262
views
matrices
nullityofmatrix
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