Recent questions tagged linear-algebra

+2 votes

1 answer

1

Ace test series

asked 5 days ago in Linear Algebra by abhishekmehta4u Boss (24.3k points) | 30 views

+1 vote

0 answers

2

Self Doubt
Relation between rank and number of non-zero eigenvalues of a matrix If Rank of n X n matrix is r, then number of non zero eigen values ?? In either of cases det(A) = 0 or if det(A) not equal 0

asked Nov 29 in Linear Algebra by jatin khachane 1 Active (3.2k points) | 23 views

0 votes

0 answers

3

Matrices
The number of binary matrices of order $N*N$ whose determinant is exactly zero.

asked Nov 29 in Linear Algebra by HeadShot Active (3.5k points) | 25 views

0 votes

1 answer

4

Gilbert_Strang_LU_Decomposition
For which numbers c is $A=LU$ impossible? $\begin{bmatrix} 1 & 2 &0 \\ 3 & c &1 \\ 0 &1 &1 \end{bmatrix}$

asked Nov 18 in Linear Algebra by Ayush Upadhyaya Boss (18.8k points) | 67 views

0 votes

1 answer

5

Cases when LU decomposition is possible.

asked Nov 18 in Linear Algebra by Ayush Upadhyaya Boss (18.8k points) | 64 views

0 votes

0 answers

6

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?

asked Nov 17 in Linear Algebra by Ayush Upadhyaya Boss (18.8k points) | 66 views

0 votes

0 answers

7

#math combat
If $A$ is $2\times 2$ matrix ,eigen value is $1,-2$ and corresponding eigen vector $[1,2]^{T}$ and $[9,1]^{T}$.find sum of element of the matrix $A.$

asked Nov 15 in Linear Algebra by amit166 Junior (529 points) | 43 views

+1 vote

1 answer

8

Linear Algebra_25
Let AX=B be a system of n linear equations in n unknown with integer coefficient and the components of B are all integer. Consider the following (1)det(A)=1 (2)det(A)=0 (3)Solution X has integer entries (4)Solution X does not have all integer entries For the given system ... then 3 holds true (c)If 1, then 4 holds true (d)If 2, then 3 holds true I think (d) should be the answer.

asked Nov 15 in Linear Algebra by Ayush Upadhyaya Boss (18.8k points) | 64 views

0 votes

0 answers

9

#books q
the number of algebric terms in expansion of a determinant of order 5 is

asked Nov 13 in Linear Algebra by amit166 Junior (529 points) | 31 views

+1 vote

1 answer

10

Eigen Vector

asked Nov 7 in Linear Algebra by Na462 Loyal (7.4k points) | 151 views

0 votes

0 answers

11

GATE-ME-2016

asked Nov 6 in Linear Algebra by aditi19 Active (2.1k points) | 53 views

0 votes

1 answer

12

linear algebra
The Eigen Vectors of the Matrix $A=\begin{bmatrix} 3 &4 \\ 4 &-3 \end{bmatrix}$ are $\begin{bmatrix} a\\ 1 \end{bmatrix},\begin{bmatrix} 1\\ b \end{bmatrix}$ the $a+b=?$ Answer is given (a+b)=0 how ?????

asked Oct 30 in Linear Algebra by altamash (313 points) | 37 views

0 votes

0 answers

13

self doubt
which method is used for solving equation as shown in image

asked Oct 29 in Linear Algebra by kd..... (481 points) | 22 views

0 votes

0 answers

14

Eigen Vector

asked Oct 26 in Linear Algebra by Na462 Loyal (7.4k points) | 29 views

0 votes

0 answers

15

Eigen Values(Matrix is not idempotent)
Given that a matrix $A_{3\times3},$which is not idempotent matrix.And $A^{3}=A.$ Then find them, $1)$ Eigen Values $2)$ Trace of the matrix$=$Sum of Leading Diagonal Elements$=\sum a_{ij},$ where $i=j$ $3)Det(A)$

asked Oct 25 in Linear Algebra by Lakshman Patel RJIT Boss (20k points) | 40 views

0 votes

1 answer

16

Rank of the matrix
Given that a matrix $[A]_{4\times4},$any one row/column is dependent on the others, and given matrix are singular matrix$(|A|=0)$. And another matrix $B=adj(A),$then find them, $1)$Rank of the matrix $B$ $2)$Rank of the marix $adj(B)$

asked Oct 25 in Linear Algebra by Lakshman Patel RJIT Boss (20k points) | 48 views

0 votes

0 answers

17

Linear algebra
Given that the matrix $A=\begin{bmatrix} a_{11} &a_{12} \\ a_{21} &a_{22} \end{bmatrix}$ and Eigen value are $1,-2$ and Corresponding Eigen Vectors are $X_{1}=\begin{bmatrix} 1\\2 \end{bmatrix}$ and $X_{2}=\begin{bmatrix} 9\\1 \end{bmatrix}$ Find the $1)\sum a_{ij},$when $i=j$ $2)Det(A)$ $3)$Sum of all Elements in the given matrix

asked Oct 25 in Linear Algebra by Lakshman Patel RJIT Boss (20k points) | 49 views

0 votes

0 answers

18

System of Equations
My solution:- Since the Determinant of matrix is Zero. So it will posses non trivial solution. Now what should be the answer ? According to me Option D as rank is < Order so infinite number of solutions

asked Oct 25 in Linear Algebra by Na462 Loyal (7.4k points) | 45 views

+2 votes

1 answer

19

Linear algebra
For matrix $p=\begin{bmatrix} 3 &-2 &2 \\ 0 &-2 &1 \\ 0& 0 & 1 \end{bmatrix}$if one of the eigen values is equal to – 2, then which of the following is an eigen vector? (a) [ 3 −2 1 ] (b) [ −3 2 −1 ] (c) [ 1 −2 3 ] (d) [ 5 2 0 ]

asked Oct 21 in Linear Algebra by sahil_malik (265 points) | 147 views

0 votes

0 answers

20

Linear algebra
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 diagonalizable

asked Oct 20 in Linear Algebra by sahil_malik (265 points) | 22 views

+1 vote

1 answer

21

number of linearly indendent eigen vectors

asked Oct 14 in Linear Algebra by MIRIYALA JEEVAN KUMA Active (2.3k points) | 70 views

0 votes

0 answers

22

Linear Algebra
We know, the eigen value for upper triangular/lower triangular/diagonal matrices are the diagonal elements of the matrix. https://gateoverflow.in/858/gate2002-5a This question, https://gateoverflow.in/1174/gate2005-49 If apply row transformation to convert it ... make the given matrix to upper triangular matrix, so that eigen values will be equal to the elements in the diagonals?

asked Oct 5 in Linear Algebra by Swapnil Naik Active (2.3k points) | 44 views

+1 vote

1 answer

23

GATE2016 37 Mathematics
Let $M = \begin{bmatrix} a & b &c \\ b &d & e\\ c & e & f \end{bmatrix}$ be a real matrix with eigenvalues 1, 0 and 3. If the eigenvectors corresponding to 1 and 0 are $\left ( 1,1,1 \right )^T$ and $\left ( 1,-1, 0 \right )^T$ respectively, then the value of 3f is equal to _______.

asked Oct 4 in Linear Algebra by Mk Utkarsh Boss (29.5k points) | 162 views

0 votes

0 answers

24

Which books are good to practice linear algebra and calculas?

asked Oct 1 in GATE by aditi19 Active (2.1k points) | 15 views

0 votes

1 answer

25

Linear Algebra RGPV 2001
Test the consistency of the following system of equations and solve if possible $3x + 3y +2z = 1$ $x + 2y = 4$ $10y + 3z = -2$ $2x - 3y -z = 5$

asked Sep 29 in Linear Algebra by Mk Utkarsh Boss (29.5k points) | 59 views

0 votes

1 answer

26

Hk Dass Linear Algebra
Test the consistency of the following system of equations $5x + 3y + 7z = 4 $ $3x + 26y + 2z = 9$ $7x + 2y + 10z = 5$

asked Sep 29 in Linear Algebra by Mk Utkarsh Boss (29.5k points) | 50 views

0 votes

1 answer

27

Linear system of equations

asked Sep 16 in Linear Algebra by Na462 Loyal (7.4k points) | 36 views

0 votes

1 answer

28

Engineering Maths
If A = $\begin{bmatrix} -1 & 1 & 0 \\ 0 & 2 &-2 \\ 0& 0 & 3 \end{bmatrix}$ then trace of the matrix 3A2 + adj A is ____

asked Aug 23 in Linear Algebra by suparna kar (121 points) | 38 views

0 votes

0 answers

29

Gate 2016 ME Set 2
The condition for which the eigen values of the matrix A = $\begin{pmatrix} 2 &1 \\ 1& k \end{pmatrix}$ are positive, is a) k>1/2 b) k>-2 c) k>0 d) k< -1/2

asked Aug 17 in Linear Algebra by suparna kar (121 points) | 61 views

0 votes

0 answers

30

Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.

asked Aug 8 in Linear Algebra by pankaj_vir Loyal (9.7k points) | 51 views

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