Recent questions and answers in Linear Algebra

+3 votes

4 answers

1

GATE2019-9
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is non-zero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements

answered 1 day ago in Linear Algebra by gaurav1.yuva (45 points) | 1.6k views

+2 votes

1 answer

2

TIFR-2015-Maths-B-13
Let $X=\left\{(x, y) \in \mathbb{R}^{2}: 2x^{2}+3y^{2}= 1\right\}$. Endow $\mathbb{R}^{2}$ with the discrete topology, and $X$ with the subspace topology. Then. $X$ is a compact subset of $\mathbb{R}^{2}$ in this topology. $X$ is a connected subset of $\mathbb{R}^{2}$ in this topology. $X$ is an open subset of $\mathbb{R}^{2}$ in this topology. None of the above.

answered Apr 8 in Linear Algebra by Sushantkala786 (11 points) | 72 views

0 votes

4 answers

3

ISRO 2012- ECE Matrices
The Eigen values of matrix are: a) ± cos∝ b) ± sin ∝ c) tan ∝ & cot ∝ d) cos ∝ ± sin ∝

answered Mar 10 in Linear Algebra by Debdeep1998 Junior (635 points) | 88 views

0 votes

3 answers

4

ISRO2012-ECE: Engineering Mathematics
The system of equations x + y + z = 6, 2x + y + z = 7, x + 2 y + z = 8 has a. A unique solution b. No solution c. An infinite number of solutions d. None of these

answered Mar 10 in Linear Algebra by abhishekmehta4u Boss (33.4k points) | 56 views

+3 votes

4 answers

5

Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix

answered Mar 10 in Linear Algebra by Verma Ashish Loyal (6.6k points) | 194 views

0 votes

1 answer

6

Ace Test Series: Linear Algebra - Eigen Values

answered Mar 9 in Linear Algebra by abhishekmehta4u Boss (33.4k points) | 135 views

0 votes

2 answers

7

ISRO 2014 -Trigonometry [EE]
If tan $\Theta$ = 8 / 15 and $\Theta$ is acute, then cosec $\Theta$ (A) 8 / 17 (B) 8 / 15 (C) 17 / 8 (D) 17 / 15

answered Mar 7 in Linear Algebra by abhishekmehta4u Boss (33.4k points) | 202 views

0 votes

0 answers

8

ISI-MMA-2015-44
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ It is given ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane

asked Feb 22 in Linear Algebra by ankitgupta.1729 Boss (10.7k points) | 60 views

0 votes

1 answer

9

Linear Algebra-METest
If the determinant of the below matrix is 245, what is the value of X? $\begin{bmatrix} 0 & 4& 2 &1 \\ 3& -1 & 0 & 2\\ 5&2 & x& 4\\ 6& 1 & -1 & 0 \end{bmatrix}$ ... , because by keeping 6 in place of x I am getting determinant as 245(Result verified by computer program). Please let me know where I am going wrong?

answered Feb 19 in Linear Algebra by Meet2698 (151 points) | 131 views

+20 votes

4 answers

10

GATE2015-2-27
Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.

answered Feb 18 in Linear Algebra by Ram Swaroop Active (2.6k points) | 1.8k views

+14 votes

3 answers

11

GATE1998-2.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &2 \end{bmatrix}$ $3$ $1$ $2$ $4$

answered Feb 18 in Linear Algebra by Ram Swaroop Active (2.6k points) | 1.6k views

+4 votes

3 answers

12

ISRO-DEC2017-17
If $C$ is a skew-symmetric matrix of order $n$ and $X$ is $n\times 1$ column matrix, then $X{^T} CX$ is a scalar matrix null matrix unit matrix matrix will all elements $1$

answered Feb 12 in Linear Algebra by Abhisek Tiwari 4 Active (4.4k points) | 1.4k views

+3 votes

3 answers

13

GATE2019-44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______

answered Feb 7 in Linear Algebra by Lakshman Patel RJIT Boss (34.5k points) | 2.1k views

+21 votes

2 answers

14

GATE2015-1-1‏8
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.

answered Feb 6 in Linear Algebra by Verma Ashish Loyal (6.6k points) | 2.6k views

0 votes

0 answers

15

Previous gate

asked Jan 31 in Linear Algebra by Hemanth_13 Loyal (6.6k points) | 70 views

0 votes

0 answers

16

#math

asked Jan 30 in Linear Algebra by amit166 Junior (761 points) | 21 views

0 votes

0 answers

17

ace test series
how? please explain

asked Jan 28 in Linear Algebra by Vignaneswarkrishna (187 points) | 40 views

0 votes

1 answer

18

Gatebook Test

answered Jan 28 in Linear Algebra by Meet2698 (151 points) | 50 views

0 votes

1 answer

19

Ace Test Series 2019: Discrete Maths - Recurrence Relation

answered Jan 27 in Linear Algebra by Meet2698 (151 points) | 66 views

0 votes

0 answers

20

Gate 2016 ee
Question number 249

asked Jan 27 in Linear Algebra by Vignaneswarkrishna (187 points) | 32 views

+14 votes

3 answers

21

GATE2004-IT-36
If matrix $X = \begin{bmatrix} a & 1 \\ -a^2+a-1 & 1-a \end{bmatrix}$ and $X^2 - X + I = O$ ($I$ is the identity matrix and $O$ is the zero matrix), then the inverse of $X$ is $\begin{bmatrix} 1-a &-1 \\ a^2& a \end{bmatrix}$ ... $\begin{bmatrix} -a &1 \\ -a^2+a-1& 1-a \end{bmatrix}$ $\begin{bmatrix} a^2-a+1 &a \\ 1& 1-a \end{bmatrix}$

answered Jan 27 in Linear Algebra by dsomnath (69 points) | 882 views

+31 votes

6 answers

22

GATE2007-IT-2
Let A be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of xT Ax where the maximum is taken over all x that are the unit eigenvectors of A? $3$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$

answered Jan 26 in Linear Algebra by Sambhrant Maurya Active (1.7k points) | 2.9k views

+1 vote

1 answer

23

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)

answered Jan 24 in Linear Algebra by Somoshree Datta 5 Active (4.8k points) | 102 views

–1 vote

0 answers

24

acetest series

asked Jan 21 in Linear Algebra by Rajesh Panwar Junior (601 points) | 52 views

0 votes

1 answer

25

Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=? a)24 b)-2 c)12 d)-12 Please explain in detail.

answered Jan 20 in Linear Algebra by Rishabh Agrawal Junior (953 points) | 83 views

0 votes

1 answer

26

Simple Determinant
how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??

answered Jan 20 in Linear Algebra by Rishabh Agrawal Junior (953 points) | 46 views

+16 votes

4 answers

27

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 Jan 19 in Linear Algebra by dnivara (37 points) | 4.9k views

0 votes

1 answer

28

MadeEasy Full Length Test 2019: Engineering Mathematics - Linear Algebra

answered Jan 17 in Linear Algebra by kd..... Junior (883 points) | 61 views

0 votes

0 answers

29

uppcl-2018
need soln [closed]

asked Jan 11 in Linear Algebra by SAUMYA2019 (105 points) | 22 views

0 votes

1 answer

30

GATEBOOK-2019 Grand Test Mathematics-10
Consider the system of equation $2x+3y+5z = 30 \\ 4x+6y+10z =40 \\ x+y -z = 2 $ The above system has No solution a unique solution More than one but finite solutions an infinite number of solutions

answered Jan 11 in Linear Algebra by pranay562 Active (1.2k points) | 51 views

0 votes

0 answers

31

made easy
The probability of a man hitting a target in one fire is 1/4 The number of times at least he must fire at the target in order that his chance of hitting the target at least once will exceed 2/3 will be _______.

asked Jan 7 in Linear Algebra by pream sagar Active (2.7k points) | 80 views

+1 vote

0 answers

32

made easy
If 2, – 4 are the eigen values of a non-singular matrix A and |A| = –8, then the eigen values of Adj A are x and –y then the value of x + y is _________.

asked Jan 7 in Linear Algebra by pream sagar Active (2.7k points) | 66 views

0 votes

0 answers

33

Doubt on syllabus
Is LU decomposition in course for GATE 2019? [closed]

asked Jan 6 in Linear Algebra by subho16 (189 points) | 40 views

0 votes

0 answers

34

GATE 2008 C.E.
The eigen values of the matrix [P] = |4 5| are? |2 -5| The answer for this is -6 and 5. My question is what wrong am I doing by R1 = R1 + R2 and converting it to lower triangular matrix. Answer after this is +6 and -5 i.e. sign of eigen values inverted.

asked Jan 6 in Linear Algebra by Barney Ross (315 points) | 37 views

0 votes

0 answers

35

UPPCL AE 2018:58

asked Jan 5 in Linear Algebra by Lakshman Patel RJIT Boss (34.5k points) | 24 views

+18 votes

2 answers

36

GATE2014-3-4
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. If the ... its eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.

answered Jan 5 in Linear Algebra by Parth Shah Junior (699 points) | 2.1k views

0 votes

0 answers

37

Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?

asked Jan 4 in Linear Algebra by Shamim Ahmed Active (2.5k points) | 79 views

0 votes

0 answers

38

Gatebook Test
[closed]

asked Jan 4 in Linear Algebra by Shadan Karim Junior (977 points) | 72 views

+1 vote

0 answers

39

Gatebook Test

asked Jan 4 in Linear Algebra by Shadan Karim Junior (977 points) | 76 views

0 votes

0 answers

40

Gatebook Test

asked Jan 4 in Linear Algebra by Shadan Karim Junior (977 points) | 34 views

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