Recent questions tagged linear-algebra

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Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?

theakatsuki4 asked in Linear Algebra 3 days ago

by theakatsuki4

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9 votes

4 answers

2

GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________

Arjun asked in Linear Algebra Feb 18

by Arjun

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2 votes

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3

GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.

Arjun asked in Linear Algebra Feb 18

by Arjun

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1 vote

1 answer

4

CMI-2018-DataScience-A: 1
If $P$ is an invertible matrix and $A=PBP^{-1},$ then which of the following statements are necessarily true? $B=P^{-1}AP$ $|A|=|B|$ $A$ is invertible if and only if $B$ is invertible $B^T=A^T$

soujanyareddy13 asked in Others Jan 29

by soujanyareddy13

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5

CMI-2018-DataScience-A: 2
Let ... $|A|=|B|$ $|C|=|D|$ $|B|=-|C|$ $|A|=-|D|$

soujanyareddy13 asked in Others Jan 29

by soujanyareddy13

135 views

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2 answers

6

CMI-2018-DataScience-A: 3
Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true? $x^Tx$ is a $3\times 3$ matrix $xx^T$ is a $3\times 3$ matrix $xx^T$ is a $1\times 1$ matrix $xx^T=x^Tx$

soujanyareddy13 asked in Others Jan 29

by soujanyareddy13

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1 answer

7

CMI-2018-DataScience-A: 4
A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0$ denotes the $2\times 2$ matrix consisting of zeros): $A^TA$ $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$ $AA^T$ $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$

soujanyareddy13 asked in Others Jan 29

by soujanyareddy13

145 views

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2 answers

8

CMI-2018-DataScience-B: 2
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Suppose $A,B$ and $C$ are $m\times m$ matrices. What does the following algorithm compute? (Here $A(i,j)$ ... .) for i=1 to m for j=1 to m for k=1 to m C(i,j)=A(i,k)*B(k,j)+C(i,j) end end end

soujanyareddy13 asked in Others Jan 29

by soujanyareddy13

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9

CMI-2018-DataScience-B: 4
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. In computing, a floating point operation (flop) is any one of the following operations ... . How does this number change if both the matrices are upper triangular?

soujanyareddy13 asked in Others Jan 29

by soujanyareddy13

67 views

1 vote

2 answers

10

CMI-2020-DataScience-B: 2
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$

soujanyareddy13 asked in Linear Algebra Jan 29

by soujanyareddy13

203 views

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2 answers

11

NIELIT 2016 MAR Scientist C - Section B: 3
The matrices $\begin{bmatrix} \cos\theta &-\sin \theta \\ \sin \theta & cos \theta \end{bmatrix}$ and $\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$ commute under the multiplication if $a=b \text{(or)} \theta =n\pi, \: n$ is an integer always never if $a\cos \theta \neq b\sin \theta$

Lakshman Patel RJIT asked in Linear Algebra Apr 2, 2020

by Lakshman Patel RJIT

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12

NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$

Lakshman Patel RJIT asked in Linear Algebra Apr 2, 2020

by Lakshman Patel RJIT

182 views

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1 answer

13

NIELIT 2016 MAR Scientist C - Section B: 9
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent

Lakshman Patel RJIT asked in Linear Algebra Apr 2, 2020

by Lakshman Patel RJIT

171 views

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14

NIELIT 2016 MAR Scientist C - Section B: 19
If product of matrix $A=\begin{bmatrix}\cos^{2}\theta &\cos \theta \sin \theta \\ \cos \theta \sin \theta &\sin ^{2} \theta& \end{bmatrix}$ ... by an odd multiple of $\pi$ even multiple of $\pi$ odd multiple of $\dfrac{\pi}{2}$ even multiple of $\dfrac{\pi}{2}$

Lakshman Patel RJIT asked in Linear Algebra Apr 2, 2020

by Lakshman Patel RJIT

207 views

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1 answer

15

NIELIT 2017 OCT Scientific Assistant A (IT) - Section B: 7
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiplied by $2,$ its determinant value becomes $40.$ The value of $’n’$ is $2$ $3$ $5$ $4$

Lakshman Patel RJIT asked in Linear Algebra Apr 1, 2020

by Lakshman Patel RJIT

228 views

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2 answers

16

NIELIT 2017 OCT Scientific Assistant A (CS) - Section C: 9
$M$ is a square matrix of order $’n’$ and its determinant value is $5.$ If all the elements of $M$ are multiple by $2,$ its determinant value becomes $40.$ The value of $’n’$ is $2$ $3$ $5$ $4$

Lakshman Patel RJIT asked in Linear Algebra Apr 1, 2020

by Lakshman Patel RJIT

375 views

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17

NIELIT 2016 MAR Scientist B - Section B: 4
What is the determinant of the matrix $\begin{bmatrix}5&3&2\\1&2&6\\3&5&10\end{bmatrix}$ $-76$ $-28$ $+28$ $+72$

Lakshman Patel RJIT asked in Linear Algebra Mar 31, 2020

by Lakshman Patel RJIT

277 views

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1 answer

18

NIELIT 2016 MAR Scientist B - Section B: 6
The system of simultaneous equations $x+2y+z=6\\2x+y+2z=6\\x+y+z=5$ has unique solution. infinite number of solutions. no solution. exactly two solutions.

Lakshman Patel RJIT asked in Linear Algebra Mar 31, 2020

by Lakshman Patel RJIT

277 views

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2 answers

19

NIELIT 2016 MAR Scientist B - Section B: 12
If $A$ and $B$ are square matrices of size $n\times n$, then which of the following statements is not true? $\det(AB)=\det(A) \det(B)$ $\det(kA)=k^n \det(A)$ $\det(A+B)=\det(A)+\det(B)$ $\det(A^T)=1/\det(A^{-1})$

Lakshman Patel RJIT asked in Linear Algebra Mar 31, 2020

by Lakshman Patel RJIT

2.8k views

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3 answers

20

NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+ \sqrt-1)$ and $3$. The determinant of $P$ is ________. $0$ $1$ $15$ $-1$

Lakshman Patel RJIT asked in Linear Algebra Mar 31, 2020

by Lakshman Patel RJIT

336 views

1 vote

2 answers

21

NIELIT 2016 DEC Scientist B (CS) - Section B: 21
Let $A,B,C,D$ be $n\times n$ matrices, each with non-zero determinant. If $ABCD=1$, then $B^{-1}$ is: $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist.

Lakshman Patel RJIT asked in Linear Algebra Mar 31, 2020

by Lakshman Patel RJIT

335 views

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1 answer

22

NIELIT 2017 DEC Scientist B - Section B: 60
Consider two matrices $M_1$ and $M_2$ with $M_1^*M_2=0$ and $M_1$ is non singular. Then which of the following is true? $M_2$ is non singular $M_2$ is null matrix $M_2$ is the identity matrix $M_2$ is transpose of $M_1$

Lakshman Patel RJIT asked in Linear Algebra Mar 30, 2020

by Lakshman Patel RJIT

256 views

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0 answers

23

Introduction to Linear Algebra 4th edition Problem Set 1.1
How many corner does a cube have in 4 dimensions? How many 3D faces? Now by observation we can tell that, an n-dimensional cube has $2^n$ corners. 1D cube which is a line have $2^1$ corners 2D cube which is a square have $2^2$ ... . but this is the question i'm not able to answer. How every N-cube have $|2n|$ cubes of dimension (N-1)?

Mk Utkarsh asked in Linear Algebra Feb 26, 2020

325 views

6 votes

2 answers

24

GATE CSE 2020 | Question: 27
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only

Arjun asked in Linear Algebra Feb 12, 2020

by Arjun

3.9k views

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