Recent questions tagged linear-algebra / GATE Overflow for GATE CSE

3 votes

1 answer

751

GeeksQuiz No of Linearly Independent Vector for Eigen value
The number of linearly independent eigen vector for eigen value 1 $\begin{bmatrix} 1 & 3 & 2 \\ 0 & 4 & 2\\ 0 &-3 & -1 \end{bmatrix}$ ... linearly independent Vector should be equal to Matrix Rank = 1 ? The ans given is No Of Unknown - Rank ( 3-1 = 2)

The number of linearly independent eigen vector for eigen value 1$\begin{bmatrix} 1 & 3 & 2 \\ 0 & 4 & 2\\ 0 &-3 & -1 \end{bmatrix}$Matrix After Substituing eigen value 1...

yg92

1.6k views

yg92 asked Feb 5, 2017

0 votes

1 answer

752

size of matrix
Calculate the size of a square matrix (n × n) where the elements are present at (i + j) ≥ n + 1 what is the size of a matrix? is it not n^2

Calculate the size of a square matrix (n × n) where the elements are present at (i + j) ≥ n + 1what is the size of a matrix? is it not n^2

Pankaj Joshi

1.2k views

Pankaj Joshi asked Feb 5, 2017

0 votes

0 answers

753

Made easy Linear algebra
Is it necessary that the lower triangular matrix should contain 1 as leading diagonal in LU decomposition? In the solution to this problem they have taken the triangular matrix diagonal as 1.

Is it necessary that the lower triangular matrix should contain 1 as leading diagonal in LU decomposition? In the solution to this problem they have taken the triangular ...

Tendua

449 views

Tendua asked Jan 30, 2017

2 votes

2 answers

754

Test by Bikram | Mock GATE | Test 2 | Question: 33
Let A represent the below matrix: $\begin{pmatrix} 1 & 0 & 3 \\ 2 & 1 & -1 \\ 1 & -1 & 1 \end{pmatrix}$ Then which among these four options are correct : $A^{3}$ $+ 3$ $A^{2}$ $+ A – 9I = 0$ $A^{3}$ $- 3$ $A^{2}$ $- A + 9I = 0$ $A^{3}$ $- 3$ $A^{2}$ $+ A + 9I = 0$ $A^{3}$+ 3$ $A^{2}$- A + 9I = 0$

Let A represent the below matrix:$\begin{pmatrix} 1 & 0 & 3 \\ 2 & 1 & -1 \\ 1 & -1 & 1 \end{pmatrix}$Then which among these four options are correct :$A^{3}$ $+ 3$ $A^{2...

Bikram

425 views

Bikram asked Jan 24, 2017

2 votes

1 answer

755

Find Matrix
A matrix has Eigen values 1 & 4 with Eigen vectors $\begin{pmatrix} 1\\ -1 \end{pmatrix}$ and $\begin{pmatrix} 2\\ 1 \end{pmatrix}$ respectively. The matrix M is ?

A matrix has Eigen values 1 & 4 with Eigen vectors $\begin{pmatrix} 1\\ -1 \end{pmatrix}$ and $\begin{pmatrix} 2\\ 1 \end{pmatrix}$ respectively. The matrix M is ?

Krunal2016

1.3k views

Krunal2016 asked Jan 22, 2017

3 votes

1 answer

756

MATRIX
Let A be a $3 \times 3$ matrix with integer entries such that $|A| =1$. What is the maximum possible number of entries of A that are even?

Let A be a $3 \times 3$ matrix with integer entries such that $|A| =1$. What is the maximum possible number of entries of A that are even?

Supremo

804 views

Supremo asked Jan 19, 2017

0 votes

0 answers

757

Linear Algebra
The system of equations 3x1 – 12x2 + 6x3 + 9x4 = 0, 6x1 + 9x2 + 21x3 + 3x4 = 0, 3x1 + 27x2 + 6x3 = 0, –3x2 + 3x4 = 0 has (1) An unique solution (2) Infinite number of solutions (3) No solution (4) Exactly four solutions

The system of equations 3x1 – 12x2 + 6x3 + 9x4 = 0, 6x1 + 9x2 + 21x3 + 3x4 = 0, 3x1 + 27x2 + 6x3 = 0, –3x2 + 3x4 = 0 has(1)An unique solution(2)Infinite number of sol...

vishwa ratna

389 views

vishwa ratna asked Jan 19, 2017

1 votes

2 answers

758

Test by Bikram | Mock GATE | Test 1 | Question: 39
Consider the following matrix: $\left [ A \right ]=$ $\begin{bmatrix} 1.5&0 &1 \\ -0.5 & 0.5& -0.5\\ -0.5& 0 & 0 \end{bmatrix}$ The eigen values of the above matrix are: $-0.5, 0.5, 1.5$ $0.5, 0.5, 1$ $1.75, -1, 0.5$ $-0.5, 0.5, -1$

Consider the following matrix:$\left [ A \right ]=$ $\begin{bmatrix} 1.5&0 &1 \\ -0.5 & 0.5& -0.5\\ -0.5& 0 & 0 \end{bmatrix}$The eigen values of the above matrix are:$-0...

Bikram

772 views

Bikram asked Jan 16, 2017

0 votes

1 answer

759

LINEAR ALGEBRA
IS ZERO THE ONLY EIGEN VALUE OF SINGULAR MATRICES??

IS ZERO THE ONLY EIGEN VALUE OF SINGULAR MATRICES??

sushmita

527 views

sushmita asked Jan 12, 2017

2 votes

1 answer

760

Rank of matrix
The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.

The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.

harshit agarwal

1.7k views

harshit agarwal asked Jan 8, 2017

1 votes

1 answer

761

GF MT 4
Is the answer and explaination given correct ?

Is the answer and explaination given correct ?

gatesjt

1.1k views

gatesjt asked Jan 7, 2017

1 votes

1 answer

762

ace-test-series subject-test
After taking |A|=0, I am getting x3+1=0 and not x3-1=0. Is it x3+1=0 or x3-1=0?

After taking |A|=0, I am getting x3+1=0 and not x3-1=0.Is it x3+1=0 or x3-1=0?

Purple

444 views

Purple asked Jan 7, 2017

2 votes

0 answers

763

Eigen vector
Why zero vector can not be eigen vector?

Why zero vector can not be eigen vector?

Sonali Rangwani

634 views

Sonali Rangwani asked Jan 4, 2017

0 votes

0 answers

764

What are normalied Eigon Vectors ?
Give normalized eigon vector for 3*3 matrix A[ij] , in general

Give normalized eigon vector for 3*3 matrix A[ij] , in general

PEKKA

298 views

PEKKA asked Jan 3, 2017

2 votes

0 answers

765

TIFR CSE 2016 | Part B | Question: 6
A subset $X$ of $\mathbb{R}^n$ is convex if for all $x, y \in X$ and all $\lambda \in (0, 1)$, we have $\lambda x + (1- \lambda)y \in X$. If $X$ is a convex set, which of the following statements is necessarily TRUE? For every $ x \in X$ ... $x \in X$, then $\lambda x \in X$ for all scalars $\lambda$ If $x, y \in X$, then $x-y \in X$

A subset $X$ of $\mathbb{R}^n$ is convex if for all $x, y \in X$ and all $\lambda \in (0, 1)$, we have $\lambda x + (1- \lambda)y \in X$. If $X$ is a convex set, which of...

go_editor

467 views

go_editor asked Dec 28, 2016

3 votes

1 answer

766

TIFR CSE 2016 | Part A | Question: 6
Which of the following statements about the eigen values of $I_n$, the $n \times n$ identity matrix (over complex numbers), is true? The eigen values are $1, \omega, \omega^2, \dots , \omega^{n-1}$, where $\omega$ is a primitive $n$-th root of unity ... there are no other eigen values The eigen values are $1, 1/2, 1/3, \dots , 1/n$ The only eigen value is $1$

Which of the following statements about the eigen values of $I_n$, the $n \times n$ identity matrix (over complex numbers), is true?The eigen values are $1, \omega, \omeg...

go_editor

602 views

go_editor asked Dec 26, 2016

3 votes

1 answer

767

TIFR CSE 2016 | Part A | Question: 3
Consider the following set of $3n$ linear equations in $3n$ ... $\mathbb{R}^{3n}$ of dimension n $S$ is a subspace of $\mathbb{R}^{3n}$ of dimension $n-1$ $S$ has exactly $n$ elements

Consider the following set of $3n$ linear equations in $3n$ variables:$\begin{matrix} x_1-x_2=0 & x_4-x_5 =0 & \dots & x_{3n-2}-x_{3n-1}=0 \\ x_2-x_3=0 & x_5-x_6=0 & & x_...

go_editor

576 views

go_editor asked Dec 26, 2016

6 votes

2 answers

768

TIFR CSE 2017 | Part A | Question: 2
For vectors $x, \: y$ in $\mathbb{R}^n$, define the inner product $\langle x, y \rangle = \Sigma^n_{i=1} x_iy_i$, and the length of $x$ to be $\| x \| = \sqrt{\langle x, x \rangle}$. Let $a, \: b$ ... $a, \: b$? Choose from the following options. ii only i and ii iii only iv only iv and v

For vectors $x, \: y$ in $\mathbb{R}^n$, define the inner product $\langle x, y \rangle = \Sigma^n_{i=1} x_iy_i$, and the length of $x$ to be $\| x \| = \sqrt{\langle x, ...

go_editor

1.6k views

go_editor asked Dec 21, 2016

8 votes

3 answers

769

GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.

Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangula...

go_editor

3.5k views

go_editor asked Dec 20, 2016

7 votes

1 answer

770

Matrix characteristic Equation:Eigen Values

KISHALAY DAS

1.4k views

KISHALAY DAS asked Dec 18, 2016

1 votes

2 answers

771

MadeEasy Test Series: Linear Algebra - Eigen Value
can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.

can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.

Nishant Arora

772 views

Nishant Arora asked Dec 15, 2016

2 votes

1 answer

772

matrix
If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?

If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?

Neal Caffery

5.3k views

Neal Caffery asked Dec 11, 2016

0 votes

1 answer

773

find the given expression

Akriti sood

500 views

Akriti sood asked Nov 29, 2016

0 votes

1 answer

774

linear algebra
what is linearly independent eigen vector ? is it a set of vectors ? or we can say a eigen vector is linearly independent or dependent?

what is linearly independent eigen vector ? is it a set of vectors ? or we can say a eigen vector is linearly independent or dependent?

Vaishali Trivedi

400 views

Vaishali Trivedi asked Nov 16, 2016

18 votes

3 answers

775

GATE CSE 1987 | Question: 1-xxiii
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above

A square matrix is singular whenever The rows are linearly independentThe columns are linearly independentThe row are linearly dependentNone of the above

makhdoom ghaya

5.7k views

makhdoom ghaya asked Nov 8, 2016

12 votes

4 answers

776

GATE CSE 1987 | Question: 1-xxi
If $a, b,$ and $c$ are constants, which of the following is a linear inequality? $ax+bcy=0$ $ax^{2}+cy^{2}=21$ $abx+a^{2}y \geq 15$ $xy+ax \geq 20$

If $a, b,$ and $c$ are constants, which of the following is a linear inequality?$ax+bcy=0$$ax^{2}+cy^{2}=21$$abx+a^{2}y \geq 15$$xy+ax \geq 20$

makhdoom ghaya

4.1k views

makhdoom ghaya asked Nov 8, 2016

2 votes

2 answers

777

Matrix Invertibility
Let A be (3×3) real matrix. Suppose 1 & -1 are two of three Eigen values of A and 18 is one of the Eigen values of A2+3A. Then [ A ] A is invertible as well as A2 + 3A is invertible [ B ] A^2+3A is invertible but A is not invertible [ C ] A is invertible but A^2+3A is not invertible [ D ] Both A & A^2+3A are not invertible

Let A be (3×3) real matrix. Suppose 1 & -1 are two of three Eigen values of A and 18 is one of the Eigen values of A2+3A. Then [ A ] A is invertible as well as A2 ...

vishal8492

691 views

vishal8492 asked Nov 7, 2016

0 votes

1 answer

778

matrix

Prateek kumar

323 views

Prateek kumar asked Oct 18, 2016

2 votes

1 answer

779

matrix

Prateek kumar

539 views

Prateek kumar asked Oct 17, 2016

1 votes

1 answer

780

matrix

Prateek kumar

698 views

Prateek kumar asked Oct 14, 2016

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