Recent questions and answers in Linear Algebra

+5 votes

1 answer

Gilbert Strang
How many n*n (0,1) matrix are invertable ? PS: original question in book is for 2*2

answered 22 hours ago in Linear Algebra by Habibkhan Veteran (89.7k points) | 43 views

+4 votes

3 answers

GATE2005-IT-3
The determinant of the matrix given below is $$\begin{bmatrix} 0 &1 &0 &2 \\ -1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& -2& 0& 1 \end{bmatrix}$$ -1 0 1 2

answered Oct 14 in Linear Algebra by Anix7 (61 points) | 488 views

+3 votes

2 answers

GATE2005-48
Consider the following system of linear equations : $$2x_1 - x_2 + 3x_3 = 1$$ $$3x_1 + 2x_2 + 5x_3 = 2$$ $$-x_1+4x_2+x_3 = 3$$ The system of equations has no solution a unique solution more than one but a finite number of solutions an infinite number of solutions

answered Oct 14 in Linear Algebra by Rishi yadav Boss (6.2k points) | 363 views

+6 votes

4 answers

GATE2015-3_15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 are $\left\{a\left(4,2,1\right) \mid a \neq 0, a \in ... a \in \mathbb{R}\right\}$ $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$

answered Oct 14 in Linear Algebra by Rishi yadav Boss (6.2k points) | 912 views

+13 votes

4 answers

GATE 2016-1-05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______

answered Oct 14 in Linear Algebra by Rishi yadav Boss (6.2k points) | 1.7k views

+4 votes

3 answers

GATE2000-1.3
The determinant of the matrix $$\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$$ 4 0 15 20

answered Oct 14 in Linear Algebra by Rishi yadav Boss (6.2k points) | 330 views

+5 votes

4 answers

GATE1994_3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$

answered Oct 14 in Linear Algebra by Anix7 (61 points) | 339 views

+7 votes

2 answers

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 Oct 13 in Linear Algebra by Priyanka Sharma (21 points) | 1k views

+1 vote

1 answer

UGCNET-Jan2017-II-1
Consider a sequence F00 defined as : F00(0) = 1, F00(1) = 1 F00(n)= $\frac{10*F_{00}(n-1)+100}{F_{00}(n-2)}$ for n ≥ 2 Then what shall be the set of values of the sequence F00 ? (1) (1, 110, 1200) (2) (1, 110, 600, 1200) (3) (1, 2, 55, 110, 600, 1200) (4) (1, 55, 110, 600, 1200)

answered Oct 12 in Linear Algebra by Priyanka Sharma (21 points) | 22 views

+3 votes

1 answer

Matrices

answered Oct 7 in Linear Algebra by sarveswara rao v Active (1.7k points) | 48 views

+1 vote

0 answers

Solution of linear equations
The number of linearly independent solutions of 'm' homogeneous linear equations in 'n' variables ..AX=0 is (n-r) where r is the rank of a matrix..could somebody explain me by giving proper reasoning as how?...Thanks

asked Oct 6 in Linear Algebra by Shivi rao (427 points) | 25 views

+7 votes

3 answers

GATE2007-27
Consider the set of (column) vectors defined by $$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$$. Which of the following is TRUE? $\left\{\left[1,-1,0\right]^ ... linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above

answered Oct 3 in Linear Algebra by Vicky rix Loyal (4.9k points) | 1k views

0 votes

0 answers

Matrix doubt
A= 1 2 2 2 1 -2 a 2 b And AAA^T = 3l I is 3*3 identity matrix a ,b can be.... A) 2,-1 B) -2,1 C) -2,-1 D) none

asked Oct 3 in Linear Algebra by Surya Dhanraj Loyal (2.9k points) | 29 views

+5 votes

3 answers

GATE2015-2_5
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.

answered Sep 27 in Linear Algebra by adactive18 (423 points) | 742 views

+4 votes

3 answers

eigen value
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is 1) $18.33$ 2) $-18.33$ 3) $18.33-9.33 i$ 4) $18.33+9.33i$

answered Sep 27 in Linear Algebra by adactive18 (423 points) | 272 views

0 votes

0 answers

gate 2008 matrices engineering maths

asked Sep 26 in Linear Algebra by Shivam Gupta 3 (29 points) | 47 views

+6 votes

2 answers

GATE2003-41
Consider the following system of linear equations $$\left( \begin{array}{ccc} 2 & 1 & -4 \\ 4 & 3 & -12 \\ 1 & 2 & -8 \end{array} \right) \left( \begin{array}{ccc} x \\ y \\ z \end{array} \right) = \ ... dependent. For how many values of $\alpha$, does this system of equations have infinitely many solutions? $0$ $1$ $2$ $3$

answered Sep 26 in Linear Algebra by adactive18 (423 points) | 987 views

0 votes

1 answer

Problem in linear algebra
How many solutions does the following system of linear equations have? X+5y = -1 x-y = 2 x+3y = 3 A. infinitely many B. two distinct solutions C. unique D. no solution

answered Sep 23 in Linear Algebra by Rupendra Choudhary Boss (5.2k points) | 33 views

0 votes

1 answer

Matrix doubt
If matrix A = 1 2 -1 -1 1 2 2 -1 1 Then find det(adj(adj A)) is a) 14^4 b)14^6 c)14^9 d)14^2

answered Sep 21 in Linear Algebra by Rupendra Choudhary Boss (5.2k points) | 48 views

+2 votes

1 answer

TIFR-2011-Maths-B-13
Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.

answered Sep 14 in Linear Algebra by Suresh Thakur (11 points) | 91 views

+5 votes

2 answers

GATE2004-27
Let $A, B, C, D$ be $n \times n$ matrices, each with non-zero determinant. If $ABCD = I$, then $B^{-1}$ is $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist

answered Sep 13 in Linear Algebra by SivarajeshA (33 points) | 938 views

0 votes

0 answers

are both will always equal or they are not equal

asked Sep 10 in Linear Algebra by sumit goyal 1 Loyal (3.1k points) | 46 views

+1 vote

1 answer

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 Sep 1 in Linear Algebra by amrendra pal Loyal (2.9k points) | 96 views

+3 votes

0 answers

GATE CE 2005 linear algebra
Consider the system of linear equations A(n*n)X(n*1) = λ(n*1) where λ is a scalar. Let (λi , Xi) be an eigen pair of an eigen value and its corresponding eigen vector for a real matrix A. Let I be a n*n unit matrix. Which one of the following ... A's inverse ) , then mod(λi)=1 for all i. (D) if (A's transpose = A) , then λi is real for all i

asked Sep 1 in Linear Algebra by vishwajit_vishnu (423 points) | 108 views

+7 votes

4 answers

GATE2011_40
Consider the matrix as given below. $$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? (A) 1, 4, 3 (B) 3, 7, 3 (C) 7, 3, 2 (D) 1, 2, 3

answered Aug 29 in Linear Algebra by Rishi yadav Boss (6.2k points) | 412 views

0 votes

0 answers

http://ee.gateoverflow.in/212/gate2016-1-2

asked Aug 26 in Linear Algebra by sid1221 Active (2.1k points) | 60 views

+1 vote

0 answers

EE,2016
Consider a $3\times 3$ matrix with every element being equal to 1 , its only non-zero eigenvalue is ....? $3\times 3 \begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bmatrix}$ now i solve in simple way .. ... 0 &0 \\ 0 & 0 &0 \end{bmatrix}$ but i got different eigen values why this happened ... i missed something ??

asked Aug 26 in Linear Algebra by sid1221 Active (2.1k points) | 47 views

+2 votes

1 answer

State true/ false (with reason) For Linear Algebra

answered Aug 24 in Linear Algebra by sandeepjkh Active (1.4k points) | 74 views

+2 votes

2 answers

Engineering mathematics
Standard books required for linear algebra and calculus for gate syllabus ?

answered Aug 23 in Linear Algebra by Warrior Boss (9.6k points) | 54 views

0 votes

4 answers

linear algebra
[closed]

answered Aug 23 in Linear Algebra by sandeepjkh Active (1.4k points) | 62 views

+4 votes

5 answers

GATE2006-IT-26
What are the eigenvalues of the matrix P given below $$P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$$ a, a -√2, a + √2 a, a, a 0, a, 2a -a, 2a, 2a

answered Aug 22 in Linear Algebra by Aashish S Active (1.6k points) | 439 views

+6 votes

2 answers

GATE2008-3
The following system of equations $$x_1 + x_2 + 2x_3 = 1$$ $$x_1 + 2x_2 + 3x_3 = 2$$ $$x_1 + 4x_2 + αx_3 = 4$$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $-1$ any real number

answered Aug 21 in Linear Algebra by Prateek K (217 points) | 729 views

+2 votes

1 answer

Matrices
If A is a non singular matrix and $\left (I - A + A^{2} - ..... + (-1)^{n}A^{n}\right ) =0$) Then $A^{-1}$ is

answered Aug 10 in Linear Algebra by Tesla! Boss (9.6k points) | 136 views

0 votes

0 answers

Gate 2007-25
[closed]

asked Aug 2 in Linear Algebra by shalini j (257 points) | 43 views

+2 votes

3 answers

GATE2012_11
Let A be the $ 2 × 2 $ matrix with elements $a\_{11} = a_{12} = a\_{21} = +1 $ and $ a\_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are (A) $1024$ and $−1024$ (B) $1024\sqrt{2}$ and $−1024 \sqrt{2}$ (C) $4 \sqrt{2}$ and $−4 \sqrt{2}$ (D) $512 \sqrt{2}$ and $−512 \sqrt{2}$

answered Aug 1 in Linear Algebra by set2018 Loyal (4.8k points) | 806 views

+1 vote

0 answers

linear algebra
[closed]

asked Aug 1 in Linear Algebra by set2018 Loyal (4.8k points) | 41 views

0 votes

1 answer

which of the statements are true for a 5*5 matrix whose all entries are 1 ?

answered Jul 31 in Linear Algebra by Kaluti Loyal (3.2k points) | 54 views

+10 votes

3 answers

GATE2014-1-5
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________

answered Jul 31 in Linear Algebra by set2018 Loyal (4.8k points) | 1.5k views

+4 votes

2 answers

GATE 2012 What is Normalised Eigen Vector ?

answered Jul 31 in Linear Algebra by set2018 Loyal (4.8k points) | 412 views

0 votes

1 answer

Math Linear Algebra
If a,b and c are constants, which of the following is a linear inequality? a) ax + bcy = 0 b) ax^2 + cy = 21 c) abx + a^2y >= 15 d) xy + ax >= 20

answered Jul 30 in Linear Algebra by Kaluti Loyal (3.2k points) | 107 views

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