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Recent questions and answers in Linear Algebra
0
votes
1
answer
1
PGEE 2018
let A and B be two n*n matrices such that they follow commutative property under multiplication operation which of the following follows commutative property 1) $A^{T} B$ 2) $B^{T} A$ 3) $A^{T} B^{T}$ 4) None
answered
2 hours
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Linear Algebra
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Sayan Bose
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iiithpgee
0
votes
2
answers
2
ISRO 2013 Polynomials [EE]
The unique polynomial P(x) of degree 2 such that: P(1) = 1, P(3) = 27, P(4) = 64 is a) 8x2 19x + 12 b) 8x2 + 19x + 12 c) 8x2 19x + 12 d) 8x2 19x  12
answered
1 day
ago
in
Linear Algebra
by
sampurnanand mishra
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123
points)

193
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isro
isroee
engineeringmathematics
0
votes
1
answer
3
Self doubt
There are 10 different balls in such way that 6 balls are white and 4 balls are black. How many different arrangements are possible such way that black ball placed before the white ball ?
answered
2 days
ago
in
Linear Algebra
by
Subarna Das
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2.7k
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engineeringmathematics
discretemathematics
+1
vote
2
answers
4
linear algebra
answered
5 days
ago
in
Linear Algebra
by
pankaj_vir
Loyal
(
6.3k
points)

43
views
0
votes
1
answer
5
gilbert strang Problem Set 2.1
Which of the following descriptions are correct? The solutions x of Ax = $\begin{bmatrix} 1 & 1 & 1\\ 1 & 0 & 2 \end{bmatrix}$ $\begin{bmatrix} x1\\ x2\\ x3 \end{bmatrix}$ = $\begin{bmatrix} 0\\ 0\\ \end{bmatrix}$ form (a) a plane. (b) a line. (c) a point. (d) a subspace. (e) the nullspace of A. (f) the column space of A
answered
Apr 13
in
Linear Algebra
by
Kushagra Chatterjee
Junior
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827
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51
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+9
votes
3
answers
6
GATE2004IT6
What values of x, y and z satisfy the following system of linear equations? $$\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}$$ x = 6, y = 3, z = 2 x = 12, y = 3, z =  4 x = 6, y = 6, z =  4 x = 12, y =  3, z = 0
answered
Apr 12
in
Linear Algebra
by
Ayush Upadhyaya
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7.7k
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682
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gate2004it
linearalgebra
systemofequations
easy
+3
votes
2
answers
7
ISRODEC20171
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$
answered
Apr 9
in
Linear Algebra
by
Soumya29
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5.2k
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2k
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isrodec2017
+8
votes
2
answers
8
GATE20021.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
answered
Apr 6
in
Linear Algebra
by
Sayed Athar
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93
points)

506
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gate2002
linearalgebra
easy
matrices
0
votes
1
answer
9
Gate 2004 Question on Linear Algebra
Can Somebody Please explain me in detail description how to calculate the number of upper triangular and lower triangular of a square matrix I read somewhere that it turns out to be ((n^2)+n) /2,Can someone please provide me with a proof
answered
Apr 2
in
Linear Algebra
by
gari
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3.2k
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58
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+2
votes
2
answers
10
Madeeasy workbook
A $3\times 3$ matrix $P$ is such that $P^3 =P$.Then the eigenvalues of $P$ are $1,1,1$ $1,0.5+j(0.886),0.5j(0.866)$ $1,0.5+j(0.866),0.5j(0.886)$ $0,1,1$
answered
Mar 31
in
Linear Algebra
by
Sambit Kumar
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2k
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50
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matrices
eigenvalue
+1
vote
2
answers
11
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 ..... $82$ $13$ $169$ $81$
answered
Mar 30
in
Linear Algebra
by
Kaluti
Loyal
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5.3k
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89
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matrices
eigenvalue
+1
vote
1
answer
12
Madeeasy workbook
Let $A$ be a $3\times 3$ matrix with Eigen values $1,1,0$.Then $\mid A^{100}+I\mid$ is...
answered
Mar 29
in
Linear Algebra
by
Kaluti
Loyal
(
5.3k
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55
views
matrices
eigen
eigenvalue
+2
votes
1
answer
13
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...........
answered
Mar 25
in
Linear Algebra
by
pankaj_vir
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6.3k
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106
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matrices
eigenvalue
+1
vote
1
answer
14
Made easy workbook
Let $A = (a_{ij})_{n\times n}$ such that $a_{ij}=3$ for all $i,j$ then nullity of $A$ is $n1$ $n3$ $n$ $0$
answered
Mar 23
in
Linear Algebra
by
abhishekmehta4u
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9.7k
points)

64
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matrices
nullityofmatrix
+3
votes
1
answer
15
Madeeasy workbook
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is $2\times 4^4$ $3\times 4^4$ $4\times 4^4$ $3\times 2^4$
answered
Mar 22
in
Linear Algebra
by
pankaj_vir
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6.3k
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66
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matrices
+1
vote
1
answer
16
Made easy Workbook
The system of equations $2x+y=5$ $x3y=1$ $3x+4y=k$ is consistent when $k =........$
answered
Mar 22
in
Linear Algebra
by
pankaj_vir
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6.3k
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51
views
+1
vote
2
answers
17
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
answered
Mar 22
in
Linear Algebra
by
Sambit Kumar
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(
2k
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43
views
matrices
–1
vote
0
answers
18
System of equations#gate 2016
[closed]
asked
Mar 15
in
Linear Algebra
by
priyanka gupta 14
(
23
points)

22
views
+1
vote
1
answer
19
Determinant
Find the determinant of the $n\times n$ matrix $\begin{bmatrix} 2cos\Theta & 1 & 0 &0 &........ & 0 & \\ 1&2cos\Theta &1 & 0 & ........ & 0 & \\ 0&1 & 2cos\Theta & 1 &........ & 0 & ... &.... & 1 & 2cos\Theta & \end{bmatrix}$ how the answer could be $D_{n}2cos\Theta D_{n1}+D_{n2}=0$? Plz explain
answered
Mar 13
in
Linear Algebra
by
ankitgupta.1729
Active
(
4.2k
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66
views
linearalgebra
matrices
0
votes
1
answer
20
ISRO 2010ECE Matrices
Which of the following is true? a) The product of the eigenvalues of a matrix is equal to the trace of the matrix b) The eigenvalues of a skewsymmetric matrix are real c) A is a nonzero column matrix and B is a nonzero row matrix, then ... equations is consistent if and only if the rank of the coefficient matrix is less than or equal to the rank of the augmented matrix
answered
Mar 13
in
Linear Algebra
by
Aishwarya Gujrathi
(
479
points)

133
views
isro
isroece
engineeringmathematics
0
votes
1
answer
21
GATE2007 EE
Let $x$ and $y$ be two vectors in a $3$ dimensional space and $<x,y>$ denote their dot product. Then the determinant $det\begin{bmatrix}<x,x> & <x,y>\\ <y,x> & <y,y>\end{bmatrix}$ is zero when $x$ and $y$ are ... positive when $x$ and $y$ are linearly independent is nonzero for all nonzero $x$ and $y$ is zero only when either $x$ or $y$ is zero
answered
Mar 13
in
Linear Algebra
by
ankitgupta.1729
Active
(
4.2k
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70
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engineeringmathematics
linearalgebra
+9
votes
2
answers
22
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
Mar 12
in
Linear Algebra
by
Sai Sankalp
(
149
points)

1.5k
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gate2018
linearalgebra
matrices
eigenvalue
normal
0
votes
1
answer
23
self doubt
if $A^{3} = 0$ can we conclude that $A^{2} = A$ that will be valid for zero matrix
answered
Mar 7
in
Linear Algebra
by
Sambit Kumar
Active
(
2k
points)

58
views
matrix
0
votes
0
answers
24
Q.9. ISRO 2007
[closed]
asked
Mar 6
in
Linear Algebra
by
kumarip
(
53
points)

61
views
+1
vote
2
answers
25
Gate CE 2005 linear algebra
Consider a non homogeneous system of linear equations representing mathematically an over determined system. Such a system will be (A) consistent having a unique solution (B) consistent having many solutions (C) inconsistent having a unique solution (D) inconsistent having no solution
answered
Mar 6
in
Linear Algebra
by
Sai Sankalp
(
149
points)

273
views
engineeringmathematics
linearalgebra
+28
votes
4
answers
26
GATE2014247
The product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
answered
Mar 5
in
Linear Algebra
by
Sai Sankalp
(
149
points)

5.5k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
0
votes
0
answers
27
self doubt
Assume λ=−1 is an eigenvalue of a 3x3 matrix A and x=[2 3 4]T is an eigenvector corresponding to this λ Find A^101x.
asked
Mar 4
in
Linear Algebra
by
Kaluti
Loyal
(
5.3k
points)

32
views
+1
vote
1
answer
28
Ee gate 2008
Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ is a real vector $[x_1,x_2]^T$ with length ${\vec{x}}$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of the following statements is correct? A. $P{\vec{x}}$ $\leq$ ${\vec{x}}$ where at ... $P{\vec{x}}$ >${\vec{x}}$ D. No relationship can be established between${\vec{x}}$ and $P{\vec{x}}$
answered
Mar 4
in
Linear Algebra
by
pilluverma123
(
269
points)

84
views
gate2008ee
engineeringmathematics
matrix
vectorspace
+5
votes
1
answer
29
matrix
answered
Mar 4
in
Linear Algebra
by
pilluverma123
(
269
points)

39
views
engineeringmathematics
matrices
0
votes
1
answer
30
IE Gate 2007
Let $A$ = $[a_{ij}]$, $1{\leq}i$, $j{\leq}n$, with $n{\geq}3$ and $a_{ij}$ = $i.j$. Then the rank of $A$ is A. $0$ B. $1$ C. $n1$ D. $n$
answered
Mar 4
in
Linear Algebra
by
pilluverma123
(
269
points)

37
views
engineeringmathematics
rankofmatrix
0
votes
0
answers
31
Gate cs 2007
Caption
[closed]
asked
Mar 4
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

28
views
0
votes
1
answer
32
linear algebra
A is m×n full rank matrix with m>n and 1 is an identity matrix. Let matrix A’ = (ATA)1 AT. Then which one of the following statement is FALSE? (a) AA’A = A (b) (AA’)2 (c) AA’A = 1 (d) AA’A = A’
answered
Mar 3
in
Linear Algebra
by
Abhisek Das
Active
(
1.2k
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28
views
0
votes
1
answer
33
IE Gate 2009
Let P ≠ 0 be a 3 × 3 real matrix. There exist linearly independent vectors x and y such that Px = 0 and Py = 0. The dimension of the range space of P is [IE: GATE2009] (a) 0 (b) 1 (c) 2 (d) 3
answered
Mar 3
in
Linear Algebra
by
pilluverma123
(
269
points)

37
views
0
votes
0
answers
34
Ee gate 2008
Let $P$ be a $2$ x $2$ real orthogonal matrix and ${\vec{x}}$ ia real vector $[x_1,x_2]^T$ with length ${\vec{x}}$ = ${(x_1^2 + x_2^2)^{1/2}}$. Then which one of the following statements is correct? A. $P{\vec{x}}$ $\leq$ ${\vec{x}}$ where at least ... $P{\vec{x}}$ >${\vec{x}}$ D. No relationship can be established between${\vec{x}}$ and $P{\vec{x}}$
[closed]
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

38
views
engineeringmathematics
matrix
0
votes
1
answer
35
diagonalizable concept
A2 − A = 0, where A is a 9×9 matrix. Then (a) A must be a zero matrix (b) A is an identity matrix (c) rank of A is 1 or 0 (d) A is diagonalizablev
answered
Mar 3
in
Linear Algebra
by
pankaj_vir
Loyal
(
6.3k
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45
views
0
votes
0
answers
36
CE gate 2005
Consider the system of equations A x (n n) (n t) = λ(n )l where, λ is a scalar. Let i i ( ,x ) λ be an eigenpair of an eigen value and its corresponding eigen vector for real matrix A. Let l be a (n n) unit matrix. Which one of the following statement is NOT correct? ... eigenpair for all i. (c) If AT = A1, then   λi = 1 for all i. (d) If AT = A, hen λi is real for all i.
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

23
views
0
votes
2
answers
37
linear algebra
If w cube root of – 1, then find value of deteminant [1 −w w2] [ −w w2 1 ] [ w2 1 w ]
answered
Mar 3
in
Linear Algebra
by
Lakshman Patel RJIT
Loyal
(
7.5k
points)

22
views
0
votes
1
answer
38
unitary matrix
A is a unitary matrix. Then eigen value of A are (a) 1, – 1 (b) 1, – i (c) i, – i (d) – 1, i
answered
Mar 3
in
Linear Algebra
by
Lakshman Patel RJIT
Loyal
(
7.5k
points)

38
views
+1
vote
1
answer
39
Eigen value of the following matrix
The eigen value of the following matrix is $\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$ $1, 1, 1$ $1, 0, 0$ $3, 0, 0$ $0, 0, 0$
answered
Mar 3
in
Linear Algebra
by
Lakshman Patel RJIT
Loyal
(
7.5k
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65
views
eigenvalue
matrices
0
votes
0
answers
40
polynomial
Let Mn×n be the set of all nsquare symmetric matrices and the characteristics polynomial of each A ∈ Mn×n is of the form: tn + tn – 2 + an –3tn−3 + ⋯ + a1t + a0. Then the dimension of Mn×n over R is (a) (n−1) n2 (b) (n−2) n2 (c) (n−1) (n+2)2 (d) (n−1)2 2
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

11
views
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