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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 ago in Linear Algebra by Sayan Bose Active (1.7k points) | 41 views

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 (123 points) | 193 views

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 Active (2.7k points) | 32 views

+1 vote

2 answers

4

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 (827 points) | 51 views

+9 votes

3 answers

6

GATE2004-IT-6
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 Loyal (7.7k points) | 682 views

+3 votes

2 answers

7

ISRO-DEC2017-1
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 Loyal (5.2k points) | 2k views

+8 votes

2 answers

8

GATE2002-1.1
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 (93 points) | 506 views

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 Active (3.2k points) | 58 views

+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 $1,1,1$ $1,0.5+j(0.886),0.5-j(0.866)$ $1,-0.5+j(0.866),-0.5-j(0.886)$ $0,1,-1$

answered Mar 31 in Linear Algebra by Sambit Kumar Active (2k points) | 50 views

+1 vote

2 answers

11

Madeeasy workbook
Let $A$ be a $3\times 3$ matrix such that $\mid A-I \mid=0$.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 (5.3k points) | 89 views

+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 points) | 55 views

+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 $B=A^4-5A^2+5I$ then trace of $A+B$ is...........

answered Mar 25 in Linear Algebra by pankaj_vir Loyal (6.3k points) | 106 views

+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 $n-1$ $n-3$ $n$ $0$

answered Mar 23 in Linear Algebra by abhishekmehta4u Loyal (9.7k points) | 64 views

+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 Loyal (6.3k points) | 66 views

+1 vote

1 answer

16

Made easy Workbook
The system of equations $2x+y=5$ $x-3y=-1$ $3x+4y=k$ is consistent when $k =........$

answered Mar 22 in Linear Algebra by pankaj_vir Loyal (6.3k points) | 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 Active (2k points) | 43 views

–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 $D_{n}-2cos\Theta D_{n-1}+D_{n-2}=0$? Plz explain

answered Mar 13 in Linear Algebra by ankitgupta.1729 Active (4.2k points) | 66 views

0 votes

1 answer

20

ISRO 2010-ECE 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 skew-symmetric 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

0 votes

1 answer

21

GATE-2007 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 non-zero for all non-zero $x$ and $y$ is zero only when either $x$ or $y$ is zero

answered Mar 13 in Linear Algebra by ankitgupta.1729 Active (4.2k points) | 70 views

+9 votes

2 answers

22

GATE2018-26
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 views

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

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

+28 votes

4 answers

26

GATE2014-2-47
The product of the non-zero 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

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

+5 votes

1 answer

29

answered Mar 4 in Linear Algebra by pilluverma123 (269 points) | 39 views

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. $n-1$ D. $n$

answered Mar 4 in Linear Algebra by pilluverma123 (269 points) | 37 views

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 points) | 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: GATE-2009] (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

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 points) | 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 eigen-pair 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? ... eigen-pair for all i. (c) If AT = A-1, 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 points) | 65 views

0 votes

0 answers

40

polynomial
Let Mn×n be the set of all n-square 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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