Recent questions in Linear Algebra

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1 answer

1

#GATE 2014 IN

asked May 12 in Linear Algebra by Aishvarya Akshaya Vi (35 points) | 22 views

+1 vote

1 answer

2

ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.

asked May 12 in Linear Algebra by akash.dinkar12 Boss (40.5k points) | 30 views

0 votes

1 answer

3

ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$

asked May 11 in Linear Algebra by akash.dinkar12 Boss (40.5k points) | 38 views

0 votes

1 answer

4

ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$

asked May 11 in Linear Algebra by akash.dinkar12 Boss (40.5k points) | 27 views

0 votes

2 answers

5

ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$

asked May 11 in Linear Algebra by akash.dinkar12 Boss (40.5k points) | 49 views

0 votes

1 answer

6

ISI2019-MMA-23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skew-symmetric matrix None of the above must necessarily hold

asked May 7 in Linear Algebra by Sayan Bose Loyal (6.9k points) | 100 views

0 votes

2 answers

7

ISI2019-MMA-15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$

asked May 7 in Linear Algebra by Sayan Bose Loyal (6.9k points) | 136 views

0 votes

1 answer

8

ISI2019-MMA-14
If the system of equations $\begin{array} ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$

asked May 7 in Linear Algebra by Sayan Bose Loyal (6.9k points) | 98 views

0 votes

2 answers

9

ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$

asked May 6 in Linear Algebra by Sayan Bose Loyal (6.9k points) | 155 views

0 votes

0 answers

10

CSIR UGC NET

asked Apr 28 in Linear Algebra by Hirak Active (2k points) | 33 views

0 votes

0 answers

11

Made Easy Engineering Maths book
The ans given is b, but i am not able to understande why. According to me the largest eigen value is 2, and therefore none of the option matches..!

asked Apr 27 in Linear Algebra by Hirak Active (2k points) | 47 views

+2 votes

1 answer

12

Vani Institute Question Bank Pg-231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$

asked Apr 25 in Linear Algebra by Hirak Active (2k points) | 71 views

0 votes

0 answers

13

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 (11.3k points) | 76 views

+3 votes

4 answers

14

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

asked Feb 7 in Linear Algebra by Arjun Veteran (400k points) | 1.7k views

+3 votes

3 answers

15

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 _______

asked Feb 7 in Linear Algebra by Arjun Veteran (400k points) | 2.2k views

0 votes

0 answers

16

Previous gate

asked Jan 31 in Linear Algebra by Hemanth_13 Loyal (6.6k points) | 75 views

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0 answers

17

#math

asked Jan 30 in Linear Algebra by amit166 Junior (761 points) | 29 views

0 votes

0 answers

18

ace test series
how? please explain

asked Jan 28 in Linear Algebra by Vignaneswarkrishna (187 points) | 45 views

0 votes

0 answers

19

Gate 2016 ee
Question number 249

asked Jan 27 in Linear Algebra by Vignaneswarkrishna (187 points) | 39 views

+1 vote

1 answer

20

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)

asked Jan 24 in Linear Algebra by Nandkishor3939 Active (1.2k points) | 116 views

–1 vote

0 answers

21

acetest series

asked Jan 21 in Linear Algebra by Rajesh Panwar Junior (605 points) | 58 views

0 votes

1 answer

22

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

asked Jan 19 in Linear Algebra by BHASHKAR (31 points) | 51 views

0 votes

1 answer

23

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.

asked Jan 19 in Linear Algebra by Reshu $ingh (369 points) | 92 views

0 votes

1 answer

24

Ace Test Series 2019: Discrete Maths - Recurrence Relation

asked Jan 17 in Linear Algebra by Rajesh Panwar Junior (605 points) | 77 views

0 votes

1 answer

25

MadeEasy Full Length Test 2019: Engineering Mathematics - Linear Algebra

asked Jan 16 in Linear Algebra by roman_1997 (163 points) | 72 views

0 votes

0 answers

26

uppcl-2018
need soln [closed]

asked Jan 11 in Linear Algebra by SAUMYA2019 (105 points) | 23 views

0 votes

0 answers

27

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) | 108 views

+1 vote

0 answers

28

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) | 75 views

0 votes

0 answers

29

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

asked Jan 6 in Linear Algebra by subho16 (189 points) | 42 views

0 votes

0 answers

30

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) | 42 views

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