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Recent questions in Linear Algebra
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Matrices, determinants,
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1
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 ?
asked
20 hours
ago
in
Linear Algebra
by
Raj Kumar 7
Junior
(
837
points)

30
views
engineeringmathematics
discretemathematics
+1
vote
2
answers
2
linear algebra
asked
3 days
ago
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

42
views
0
votes
1
answer
3
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
asked
Apr 11
in
Linear Algebra
by
Sambit Kumar
Active
(
2k
points)

50
views
0
votes
1
answer
4
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
asked
Apr 2
in
Linear Algebra
by
Sayed Athar
(
93
points)

58
views
+2
votes
1
answer
5
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
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

106
views
matrices
eigenvalue
+3
votes
1
answer
6
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
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

65
views
matrices
+1
vote
1
answer
7
Made easy Workbook
The system of equations $2x+y=5$ $x3y=1$ $3x+4y=k$ is consistent when $k =........$
asked
Mar 22
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

51
views
+1
vote
1
answer
8
Madeeasy workbook
Let $A$ be a $3\times 3$ matrix with Eigen values $1,1,0$.Then $\mid A^{100}+I\mid$ is...
asked
Mar 22
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

55
views
matrices
eigen
eigenvalue
+2
votes
2
answers
9
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
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

50
views
matrices
eigenvalue
+1
vote
2
answers
10
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
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

89
views
matrices
eigenvalue
+1
vote
2
answers
11
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
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

43
views
matrices
+1
vote
1
answer
12
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
in
Linear Algebra
by
Avik Chowdhury
Junior
(
539
points)

64
views
matrices
nullityofmatrix
–1
vote
0
answers
13
System of equations#gate 2016
[closed]
asked
Mar 15
in
Linear Algebra
by
priyanka gupta 14
(
23
points)

22
views
+1
vote
1
answer
14
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
asked
Mar 13
in
Linear Algebra
by
srestha
Veteran
(
81.7k
points)

65
views
linearalgebra
matrices
0
votes
1
answer
15
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
asked
Mar 13
in
Linear Algebra
by
Aishwarya Gujrathi
(
479
points)

70
views
engineeringmathematics
linearalgebra
0
votes
0
answers
16
Q.9. ISRO 2007
[closed]
asked
Mar 6
in
Linear Algebra
by
kumarip
(
53
points)

61
views
0
votes
1
answer
17
self doubt
if $A^{3} = 0$ can we conclude that $A^{2} = A$ that will be valid for zero matrix
asked
Mar 4
in
Linear Algebra
by
Kaluti
Loyal
(
5.3k
points)

57
views
matrix
0
votes
0
answers
18
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
0
votes
0
answers
19
Gate cs 2007
Caption
[closed]
asked
Mar 4
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

28
views
+1
vote
1
answer
20
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 $P{\vec{x}}$
asked
Mar 4
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

84
views
gate2008ee
engineeringmathematics
matrix
vectorspace
0
votes
1
answer
21
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. $n$
asked
Mar 4
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

37
views
engineeringmathematics
rankofmatrix
0
votes
0
answers
22
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
0
answers
23
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
1
answer
24
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
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

37
views
+1
vote
1
answer
25
Eigen value of the following matrix
The eigen value of the following matrix is $\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$ $1, 1, 1$ $1, 0, 0$ $3, 0, 0$ $0, 0, 0$
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

65
views
eigenvalue
matrices
0
votes
1
answer
26
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
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

45
views
0
votes
1
answer
27
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
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

38
views
0
votes
0
answers
28
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
0
votes
0
answers
29
characteristics polynomial
A is 5×5 matrix, all of whose entries are 1, then (a) A is not diagonalizable (b) A is idempotent (c) A is nilpotent (d) The minimal polynomial and the characteristics polynomial of A are not equal
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

17
views
0
votes
1
answer
30
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’
asked
Mar 3
in
Linear Algebra
by
Prince Sindhiya
(
355
points)

28
views
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