Recent questions and answers in Linear Algebra - GATE CSE Doubts

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Ace Practice questions Linear Algebra
If ‘A’ is a non singular matrix and $(I-A^{2}+A-.....+(-1)^{n}A^{n})=0$ then $A^{-1}$ = _______________

asked 22 hours ago in Linear Algebra by Pratyush Priyam Kuan (392 points) | 4 views

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ACE Mock Test Sets
Question: One quarter of 5 element subsets of {1,2,3,4,….n} contain 7, then n = ? My answer: $\frac{C(n-1,4)}{C(n,5)} = \frac{1}{4} \Rightarrow n = 20$ Given answer: $\frac{C(n,4)}{C(n,5)} = \frac{1}{4} \Rightarrow n = 24$ I think I am correct because once we consider 7 as an element we can choose only 4 remaining elements, but can you please confirm the same?

asked Dec 5 in Linear Algebra by tamaldeepmaity (8 points) | 6 views

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#math test questions
solve this

asked Dec 5 in Linear Algebra by amit166 (113 points) | 4 views

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#doubt in linear algebra
# Eigenvectors of real symmetric matrices are orthogonal .

asked Dec 5 in Linear Algebra by amit166 (113 points) | 4 views

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MOCK TESTS GATEFORUM
The matrix A has (1, 2, 1)^T and (1, 1, 0)^T as eigenvectors, both with eigenvalue 7, and its trace is 2. The determinant of A is __________ . (A) 84 (B) 588 (C) 49 (D) None of these

asked Dec 3 in Linear Algebra by Dipanshu Rana (24 points) | 4 views

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1 answer

GATE GURU:LINEAR ALGEBRA

answered Nov 14 in Linear Algebra by Verma Ashish (386 points) | 32 views

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GATE GURU: LA
How to approach these kind of sums? A9 means $A^9$

answered Nov 10 in Linear Algebra by Satbir (3.7k points) | 24 views

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Gate 2014 IN
A scalar valued function is defined as $F(X)=X^{T}AX+B^{T}X+C$ where A is symmetric positive definite matrix with dimension n*n; B and X are vector of dimension n *1.the minimum value of f(X) will occur when X Equal.

asked Nov 10 in Linear Algebra by amit166 (113 points) | 8 views

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Gate 2014 EE
$A=\begin{bmatrix} & 0 &1&-1& \\ & -6&-11&6& \\ & -6&-11&5 & \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is

asked Nov 10 in Linear Algebra by amit166 (113 points) | 14 views

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ACE Test Series: Matrix
If $Adj$ $A=\begin{bmatrix} -18 &-11&-10 \\ 2 & 14 &-4 \\ 4 & 5 & -8 \end{bmatrix}$, then absolute value of determinant of $A$ is __________

asked Nov 10 in Linear Algebra by srestha (558 points) | 17 views

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Gate 98 CE questions
The real symmetric matrix C corresponding to the quadratic form $Q=x_{1}x_{2}-5x_{2}x_{2}$ is

asked Nov 9 in Linear Algebra by amit166 (113 points) | 3 views

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homogeneous linear equation doubt
I have a doubt it may be simple but I am not able to understand . so, please help In homogeneous linear equation if r is the rank of the matrix. We know that row rank=column rank=rank of the matrix. My doubt is here the number of ... so number of independent variable is r .so how is the number of independent solutions is n-r. Please someone clear this doubt .

asked Nov 1 in Linear Algebra by Pratyush Priyam Kuan (392 points) | 14 views

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GRADE UP: FREE test

answered Oct 22 in Linear Algebra by Verma Ashish (386 points) | 26 views

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GATE GURU TEST SERIES: LINEAR ALGEBRA

answered Oct 21 in Linear Algebra by Satbir (3.7k points) | 37 views

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MADE EASY: LINEAR ALGEBRA

answered Oct 21 in Linear Algebra by GAITONDE (1.6k points) | 18 views

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Testbook Test series: Linear algebra
Let M be a 3 x 3 matrix such that M$\begin{pmatrix} -2\\ 1\\ 0 \end{pmatrix}$=$\begin{pmatrix} 6\\ -3\\ 0 \end{pmatrix}$ and suppose that $M^{3}$\begin{pmatrix} 1\\ -1/2\\ 0 \end{pmatrix}$=$\begin{pmatrix} \alpha\\ \beta\\ \gamma\\ \end{pmatrix}$ for some $\alpha$,$\beta$,$\gamma$ $\epsilon$ R. Then |$\alpha$| is equal to:

asked Oct 16 in Linear Algebra by Kushagra गुप्ता (155 points) | 31 views

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Gate 2007 - IN
$\\ A\ is\ n*n \ matrix \ such \ that \ A^2=I \ and B \ is \ n*1 \ real \ \\vector \ then \ Ax=B \ has \\ \\ a) no \ solution \\ b) unique \ solution\\ c) infinitely \ many \ solution\\ d) none$

answered Sep 23 in Linear Algebra by aditi19 (54 points) | 12 views

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2 answers

Nullity of a matrix
Answer is given as 1. Please show the solution. Thank you.

answered Sep 23 in Linear Algebra by aditi19 (54 points) | 17 views

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Self doubt in matrices.
A hermitian matrix can be similar to a non hermitian matrix . (True or false)?

asked Sep 17 in Linear Algebra by Eleph knaught (7 points) | 14 views

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CSIR / UGC NET - Linear Algebra
Let A be a 3x3 real matrix. Suppose 1 and -1 are two of the three Eigen values of A and 18 is one of the Eigen values of $A^2 + 3A$. Then. a) Both A and $A^2 + 3A$ are invertible b) $A^2 + 3A$ is invertible but A is not c) A is invertible but $A^2 + 3A$ is not d) Both A and $A^2 + 3A$ are not invertible [closed]

asked Sep 11 in Linear Algebra by Kushagra गुप्ता (155 points) | 7 views

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Linear algebra by Fuzhen- Zhang
Find the value of $t$ for which the following matrix has rank $3$. $\begin{pmatrix} t & 1& 1& 1 \\ 1 & t & 1& 1 \\ 1 & 1 & t & 1 \\ 1 & 1 & 1 & t \end{pmatrix}$

asked Sep 7 in Linear Algebra by Eleph knaught (7 points) | 16 views

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2 answers

Please suggest how many nd wht topic to study in group theory for gate?

answered Aug 28 in Linear Algebra by Bikram (1.2k points) | 19 views

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Eigen Value of Symmetric Matrix vs Real Symmetric Matrix

asked Aug 19 in Linear Algebra by nadeshseen (43 points) | 9 views

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1 answer

number of linearly independent eigen vectors
The number of linearly independent eigen vectors of $\begin{pmatrix} 2 & 1\\ 0 & 2 \end{pmatrix}$ The answer is 1. Please show the solution. Thank you.

answered Aug 11 in Linear Algebra by Satbir (3.7k points) | 14 views

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Group theory - order of non abelian
Let G be a non abelian group, order of G can be 24 44 54 34 Can someone explain ?

asked Aug 8 in Linear Algebra by user2525 (1.6k points) | 9 views

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#madeeasy testseries
Caption

asked Jul 20 in Linear Algebra by Pradeep Verma (10 points) | 10 views

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1 answer

ace test series self doubt
Are eigen vectors linearly dependent if we get the same eigen values??Please explain through an example

answered Jul 10 in Linear Algebra by Verma Ashish (386 points) | 18 views

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