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Recent questions tagged linear-algebra
0
votes
1
answer
91
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
379
views
nielit2017oct-assistanta-it
linear-algebra
matrix
determinant
0
votes
2
answers
92
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
844
views
nielit2017oct-assistanta-cs
engineering-mathematics
linear-algebra
matrix
determinant
1
vote
1
answer
93
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
451
views
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
determinant
2
votes
1
answer
94
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
478
views
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
system-of-equations
1
vote
2
answers
95
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
5.8k
views
nielit2016mar-scientistb
engineering-mathematics
linear-algebra
determinant
2
votes
3
answers
96
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
562
views
nielit2016dec-scientistb-it
engineering-mathematics
linear-algebra
determinant
eigen-value
1
vote
2
answers
97
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
512
views
nielit2016dec-scientistb-cs
engineering-mathematics
linear-algebra
matrix
determinant
0
votes
1
answer
98
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
362
views
nielit2017dec-scientistb
engineering-mathematics
linear-algebra
matrix
0
votes
0
answers
99
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
by
Mk Utkarsh
521
views
linear-algebra
7
votes
2
answers
100
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
6.0k
views
gatecse-2020
linear-algebra
matrix
2-marks
1
vote
1
answer
101
TIFR CSE 2020 | Part A | Question: 5
Let $A$ be am $n\times n$ invertible matrix with real entries whose column sums are all equal to $1$. Consider the following statements: Every column in the matrix $A^{2}$ sums to $2$ Every column in the matrix $A^{3}$ sums to $3$ Every column in the matrix ... $(1)$ or $(2)$ all the $3$ statements $(1),(2),$ and $(3)$ are correct
Lakshman Patel RJIT
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Patel RJIT
676
views
tifr2020
engineering-mathematics
linear-algebra
matrix
0
votes
0
answers
102
TIFR CSE 2020 | Part A | Question: 3
Let $d\geq 4$ and fix $w\in \mathbb{R}.$ Let $S = \{a = (a_{0},a_{1},\dots ,a_{d})\in \mathbb{R}^{d+1}\mid f_{a}(w) = 0\: \text{and}\: f'_{a}(w) = 0\},$ where the polynomial function $f_{a}(x)$ ... $d$-dimensional vector subspace of $\mathbb{R}^{d+1}$ $S$ is a $(d-1)$-dimensional vector subspace of $\mathbb{R}^{d+1}$ None of the other options
Lakshman Patel RJIT
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Patel RJIT
467
views
tifr2020
engineering-mathematics
linear-algebra
vector-space
2
votes
1
answer
103
TIFR CSE 2020 | Part A | Question: 2
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
Lakshman Patel RJIT
asked
in
Linear Algebra
Feb 10, 2020
by
Lakshman Patel RJIT
996
views
tifr2020
engineering-mathematics
linear-algebra
rank-of-matrix
eigen-value
3
votes
3
answers
104
ISI2014-DCG-8
If $M$ is a $3 \times 3$ matrix such that $\begin{bmatrix} 0 & 1 & 2 \end{bmatrix}M=\begin{bmatrix}1 & 0 & 0 \end{bmatrix}$ and $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} -1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
529
views
isi2014-dcg
linear-algebra
matrix
3
votes
1
answer
105
ISI2014-DCG-9
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta=1, -2$ $\eta=-1, -2$ $\eta=3, -3$ $\eta=1, 2$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
387
views
isi2014-dcg
linear-algebra
system-of-equations
1
vote
1
answer
106
ISI2014-DCG-25
The determinant $\begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix}$ equals $\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ ... $3\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ None of these
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
319
views
isi2014-dcg
linear-algebra
determinant
3
votes
1
answer
107
ISI2014-DCG-38
Suppose that $A$ is a $3 \times 3$ real matrix such that for each $u=(u_1, u_2, u_3)’ \in \mathbb{R}^3, \: u’Au=0$ where $u’$ stands for the transpose of $u$. Then which one of the following is true? $A’=-A$ $A’=A$ $AA’=I$ None of these
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
353
views
isi2014-dcg
linear-algebra
matrix
1
vote
1
answer
108
ISI2014-DCG-64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & -4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $-3$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
411
views
isi2014-dcg
linear-algebra
matrix
system-of-equations
0
votes
0
answers
109
ISI2014-DCG-70
For the matrices $A = \begin{pmatrix} a & a \\ 0 & a \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$, $(B^{-1}AB)^3$ is equal to $\begin{pmatrix} a^3 & a^3 \\ 0 & a^3 \end{pmatrix}$ ... $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$ $\begin{pmatrix} a^3 & 0 \\ -3a^3 & a^3 \end{pmatrix}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
268
views
isi2014-dcg
linear-algebra
matrix
inverse
1
vote
1
answer
110
ISI2015-MMA-37
Let $a$ be a non-zero real number. Define $f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is $1$ $2$ $3$ $4$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
631
views
isi2015-mma
linear-algebra
determinant
functions
0
votes
0
answers
111
ISI2015-MMA-38
A real $2 \times 2$ matrix $M$ such that $M^2 = \begin{pmatrix} -1 & 0 \\ 0 & -1- \varepsilon \end{pmatrix}$ exists for all $\varepsilon > 0$ does not exist for any $\varepsilon > 0$ exists for some $\varepsilon > 0$ none of the above is true
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
432
views
isi2015-mma
linear-algebra
matrix
7
votes
3
answers
112
ISI2015-MMA-39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
715
views
isi2015-mma
linear-algebra
matrix
eigen-value
0
votes
0
answers
113
ISI2015-MMA-40
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define a $4 \times 4$ matrix $\textbf{A}$ ... $(\textbf{A})$ equals $1$ or $2$ $0$ $4$ $2$ or $3$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
423
views
isi2015-mma
linear-algebra
matrix
rank-of-matrix
2
votes
2
answers
114
ISI2015-MMA-42
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & - \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{ - \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ - \frac{\pi}{3}, \frac{\pi}{3} \}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
606
views
isi2015-mma
linear-algebra
matrix
eigen-value
1
vote
1
answer
115
ISI2015-MMA-43
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta = 1, -2$ $\eta = -1, -2$ $\eta = 3, -3$ $\eta = 1, 2$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
369
views
isi2015-mma
linear-algebra
system-of-equations
0
votes
3
answers
116
ISI2015-MMA-44
Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by $\begin{array} {} a_1x +b_1y+c_1z=\alpha _1 \\ a_2x +b_2y+c_2z=\alpha _2 \\ a_3x +b_3y+c_3z=\alpha _3 \end{array}$ It is given that $P_1$, $P_2$ and $P_3$ ... then the planes do not have any common point of intersection intersect at a unique point intersect along a straight line intersect along a plane
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
550
views
isi2015-mma
linear-algebra
system-of-equations
2
votes
1
answer
117
ISI2015-MMA-61
Let $ A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{pmatrix} \text{ and } B=\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{pmatrix}.$ Then there exists a matrix $C$ ... no matrix $C$ such that $A=BC$ there exists a matrix $C$ such that $A=BC$, but $A \neq CB$ there is no matrix $C$ such that $A=CB$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
401
views
isi2015-mma
linear-algebra
matrix
2
votes
1
answer
118
ISI2015-MMA-62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
590
views
isi2015-mma
linear-algebra
matrix
eigen-value
1
vote
2
answers
119
ISI2015-MMA-63
Let $\theta=2\pi/67$. Now consider the matrix $A = \begin{pmatrix} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{pmatrix}$. Then the matrix $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
431
views
isi2015-mma
linear-algebra
matrix
0
votes
2
answers
120
ISI2015-DCG-3
The value of $\begin{vmatrix} 1+a & 1 & 1 & 1 \\ 1 & 1+b & 1 & 1 \\ 1 & 1 & 1+c & 1 \\ 1 & 1 & 1 & 1+d \end{vmatrix}$ is $abcd(1+\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d})$ $abcd(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d})$ $1+\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}$ None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
371
views
isi2015-dcg
linear-algebra
determinant
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