Recent questions and answers in Linear Algebra

0 votes

0 answers

1

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 1 day ago in Linear Algebra by ankitgupta.1729 Loyal (9.4k points) | 19 views

0 votes

1 answer

2

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 4 days ago in Linear Algebra by Meet2698 (133 points) | 106 views

+20 votes

4 answers

3

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 5 days ago in Linear Algebra by Ram Swaroop Active (2.3k points) | 1.7k views

+14 votes

3 answers

4

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 5 days ago in Linear Algebra by Ram Swaroop Active (2.3k points) | 1.5k views

+4 votes

3 answers

5

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 (3.9k points) | 1.3k views

+2 votes

3 answers

6

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 Feb 7 in Linear Algebra by Sukhbir Singh (309 points) | 1.5k views

+2 votes

3 answers

7

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 (29k points) | 1.9k views

+21 votes

2 answers

8

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 Active (4.7k points) | 2.6k views

0 votes

0 answers

9

Previous gate

asked Jan 31 in Linear Algebra by Hemanth_13 Loyal (6.5k points) | 65 views

0 votes

0 answers

10

#math

asked Jan 30 in Linear Algebra by amit166 Junior (693 points) | 19 views

0 votes

0 answers

11

ace test series
how? please explain

asked Jan 28 in Linear Algebra by Vignaneswarkrishna (167 points) | 36 views

0 votes

1 answer

12

Gatebook Test

answered Jan 28 in Linear Algebra by Meet2698 (133 points) | 45 views

0 votes

1 answer

13

Ace test series

answered Jan 27 in Linear Algebra by Meet2698 (133 points) | 55 views

0 votes

0 answers

14

Gate 2016 ee
Question number 249

asked Jan 27 in Linear Algebra by Vignaneswarkrishna (167 points) | 25 views

+14 votes

3 answers

15

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) | 860 views

+3 votes

3 answers

16

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

answered Jan 27 in Linear Algebra by askeshavas (157 points) | 131 views

+30 votes

6 answers

17

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 (1.5k points) | 2.9k views

+1 vote

1 answer

18

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 (4.6k points) | 78 views

–1 vote

0 answers

19

acetest series

asked Jan 21 in Linear Algebra by Rajesh Panwar Junior (601 points) | 46 views

0 votes

1 answer

20

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) | 61 views

0 votes

1 answer

21

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) | 36 views

+16 votes

4 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 Jan 19 in Linear Algebra by dnivara (37 points) | 4.8k views

0 votes

1 answer

23

Made easy

answered Jan 17 in Linear Algebra by kd..... Junior (851 points) | 43 views

0 votes

0 answers

24

uppcl-2018
need soln [closed]

asked Jan 11 in Linear Algebra by SAUMYA2019 (97 points) | 20 views

0 votes

1 answer

25

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) | 46 views

0 votes

0 answers

26

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 (1.7k points) | 40 views

+1 vote

0 answers

27

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 (1.7k points) | 62 views

0 votes

0 answers

28

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

asked Jan 6 in Linear Algebra by subho16 (149 points) | 38 views

0 votes

0 answers

29

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 (235 points) | 32 views

0 votes

0 answers

30

UPPCL AE 2018:58

asked Jan 5 in Linear Algebra by Lakshman Patel RJIT Boss (29k points) | 22 views

+18 votes

2 answers

31

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 (597 points) | 2k views

0 votes

0 answers

32

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 (2.3k points) | 73 views

0 votes

0 answers

33

Gatebook Test
[closed]

asked Jan 4 in Linear Algebra by Shadan Karim Junior (979 points) | 70 views

+1 vote

0 answers

34

Gatebook Test

asked Jan 4 in Linear Algebra by Shadan Karim Junior (979 points) | 73 views

0 votes

0 answers

35

Gatebook Test

asked Jan 4 in Linear Algebra by Shadan Karim Junior (979 points) | 32 views

+1 vote

0 answers

36

Gatebook Test

asked Jan 4 in Linear Algebra by Shadan Karim Junior (979 points) | 32 views

+1 vote

0 answers

37

rc test series
If A=$\begin{bmatrix} 1 & 2\\ -1& 3 \end{bmatrix}$ then $\ A^{6} -4A^{5}+8A^{4}-12A^{3}+14A^{2}$=? a)0 b)4A c)4A+5I d)-4A+5I am gettind d

asked Jan 3 in Linear Algebra by Gate Fever Active (4.7k points) | 54 views

0 votes

0 answers

38

GEEKS 4 GEEKS - gate cs mock 2018
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix ? 7/4 1/7 7 4/7 Answer given : 7/4 My answer : 7 trace of a matrix is the sum of its diagonal elements.So on transposing the matrix the diagonal elements will ... is also equal to sum of eigen values.So trace of A = 7 So trace of transpose(A) should be 7. Is my reasoning right?

asked Jan 3 in Linear Algebra by vk_9_1_9 (123 points) | 46 views

0 votes

0 answers

39

Uppcl 2018
what could be the eigen values of a 2*2 Matrix if all its elements are intergers.

asked Jan 2 in Linear Algebra by Shashi Shekhar 1 Junior (557 points) | 53 views

+26 votes

4 answers

40

GATE2006-23
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows

answered Jan 2 in Linear Algebra by SameekshaGupta Junior (539 points) | 1.9k views

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