Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

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\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
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Recent questions in Linear Algebra

47 votes

8 answers

691

GATE CSE 2017 Set 2 | Question: 52
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is $2,$ then the largest among the absolute values of the eigenvalues of $M$ is _______

If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \ma...

Madhav

15.6k views

Madhav asked Feb 14, 2017

33 votes

2 answers

692

GATE CSE 2017 Set 2 | Question: 22
Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .

Let $P = \begin{bmatrix}1 & 1 & -1 \\2 & -3 & 4 \\3 & -2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}-1 & -2 &-1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices.Th...

Arjun

11.9k views

Arjun asked Feb 14, 2017

88 votes

6 answers

693

GATE CSE 2017 Set 1 | Question: 31
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements. One eigenvalue must be in $\left [ -5,5 \right ]$ The eigenvalue ... than $5$ Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II

Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements.One eigenvalu...

Arjun

49.6k views

Arjun asked Feb 14, 2017

30 votes

5 answers

694

GATE CSE 2017 Set 1 | Question: 30
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$

Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $...

Arjun

14.1k views

Arjun asked Feb 14, 2017

67 votes

9 answers

695

GATE CSE 2017 Set 1 | Question: 3
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ ... has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. no solution infinitely many solutions finitely many solutions

Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$.Consider the set of linear equations$...

Arjun

20.4k views

Arjun asked Feb 14, 2017

1 votes

1 answer

696

Test by Bikram | Mock GATE | Test 3 | Question: 54
Consider a matrix: $A =$ $\begin{bmatrix} 6 & 10\\ -2&-3 \end{bmatrix}$ The trace of $A^{10}$ is ______.

Consider a matrix: $A =$ $\begin{bmatrix} 6 & 10\\ -2&-3 \end{bmatrix}$ The trace of $A^{10}$ is ______.

Bikram

621 views

Bikram asked Feb 9, 2017

6 votes

6 answers

697

Gate ECE 2017 Eigen Value
For the given matrix A, one of the Eigenvalue is real $A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$ The real Eigen value is:

For the given matrix A, one of the Eigenvalue is real$A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$The ...

yg92

5.4k views

yg92 asked Feb 8, 2017

3 votes

1 answer

698

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

699

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

1.1k views

Pankaj Joshi asked Feb 5, 2017

0 votes

0 answers

700

gatebook
Here rank is less than no of variables why can't option A??

Here rank is less than no of variables why can't option A??

Niharika 1

268 views

Niharika 1 asked Feb 2, 2017

0 votes

0 answers

701

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

439 views

Tendua asked Jan 30, 2017

0 votes

0 answers

702

binary operation?
plz explain the meaning of question

plz explain the meaning of question

Supremo

389 views

Supremo asked Jan 28, 2017

0 votes

2 answers

703

#Testbook- 3 Qno-13
is it given correct answer ????

is it given correct answer ????

Hradesh patel

618 views

Hradesh patel asked Jan 27, 2017

0 votes

0 answers

704

Testbook
#plz check???

#plz check???

Hradesh patel

332 views

Hradesh patel asked Jan 27, 2017

1 votes

1 answer

705

Matrix
Given A = $\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}$ And AAAT = 3I I is a 3x3 identity matrix. (a,b) can be: A. (2,-1) B. (-2,1) C. (-2,-1) D. (2,1) How to solve it fast?

Given A = $\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}$And AAAT = 3II is a 3x3 identity matrix.(a,b) can be:A. (2,-1)B. (-2,1)C. (-2,-1)D. (2,1)How to solv...

Samujjal Das

506 views

Samujjal Das asked Jan 24, 2017

2 votes

1 answer

706

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

0 votes

0 answers

707

Matrix
1. If the row reduced form of a matrix has more than two non-zero entries in a row, then the corresponding system of equations has infinitely many solutions. 2. If the row reduced form of a matrix has more than two non-zero entries in a row, then the ... many solutions or no solution. The given statements are respectively A. True, True B. True, False C. False, True D. False, False

1. If the row reduced form of a matrix has more than two non-zero entries in a row, then the corresponding system of equations has infinitely many solutions.2. If the row...

Samujjal Das

400 views

Samujjal Das asked Jan 18, 2017

2 votes

2 answers

708

matrix groups
Which of the following is true? Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers. Every diagonal matrix is group under multiplication operation, where all elements of diagonal are non zero numbers. Every ... addition operation where all elements are real numbers. Both (a) and b) isn't a b c all are correct?

Which of the following is true?Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers.Every diagonal ma...

Pankaj Joshi

1.2k views

Pankaj Joshi asked Jan 12, 2017

2 votes

1 answer

709

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

710

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

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