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Webpage for Linear Algebra
Recent questions tagged linear-algebra
0
votes
1
answer
121
ISI2015-DCG-5
If $f(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then the value of $\big(f(x)\big)^2$ is $f(x)$ $f(2x)$ $2f(x)$ None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
301
views
isi2015-dcg
linear-algebra
matrix
1
vote
1
answer
122
ISI2015-DCG-11
Let two systems of linear equations be defined as follows: $\begin{array} {} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ ... $P$ and $Q$ are inconsistent $P$ and $Q$ are consistent $P$ is consistent but $Q$ is inconsistent None of the above
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
267
views
isi2015-dcg
linear-algebra
system-of-equations
0
votes
3
answers
123
ISI2015-DCG-22
The value of $\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$ is $0$ $1$ $-1$ None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
316
views
isi2015-dcg
linear-algebra
determinant
2
votes
1
answer
124
ISI2015-DCG-31
Let $A$ be an $n \times n$ matrix such that $\mid A^{2} \mid\: =1$. Here $\mid A \mid $ stands for determinant of matrix $A$. Then $\mid A \mid =1$ $\mid A \mid =0 \text{ or } 1$ $\mid A \mid =-1, 0 \text{ or } 1$ $\mid A \mid =-1 \text{ or } 1$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
289
views
isi2015-dcg
linear-algebra
matrix
determinant
0
votes
1
answer
125
ISI2015-DCG-32
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is $\begin{Bmatrix} \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
508
views
isi2015-dcg
linear-algebra
matrix
eigen-vectors
1
vote
1
answer
126
ISI2015-DCG-33
Suppose $A$ and $B$ are orthogonal $n \times n$ matrices. Which of the following is also an orthogonal matrix? Assume that $O$ is the null matrix of order $n \times n$ and $I$ is the identity matrix of order $n$. $AB-BA$ $\begin{pmatrix} A & O \\ O & B \end{pmatrix}$ $\begin{pmatrix} A & I \\ I & B \end{pmatrix}$ $A^2 – B^2$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
286
views
isi2015-dcg
linear-algebra
matrix
orthogonal-matrix
1
vote
1
answer
127
ISI2015-DCG-34
Let $A_{ij}$ denote the minors of an $n \times n$ matrix $A$. What is the relationship between $\mid A_{ij} \mid $ and $\mid A_{ji} \mid $? They are always equal $\mid A_{ij} \mid = – \mid A _{ji} \mid \text{ if } i \neq j$ They are equal if $A$ is a symmetric matrix If $\mid A_{ij} \mid =0$ then $\mid A_{ji} \mid =0$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
224
views
isi2015-dcg
linear-algebra
matrix
determinant
0
votes
1
answer
128
ISI2016-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
212
views
isi2016-dcg
linear-algebra
determinant
0
votes
1
answer
129
ISI2016-DCG-4
If $f(x)=\begin{bmatrix}\cos\:x & -\sin\:x & 0 \\ \sin\:x & \cos\:x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then the value of $\big(f(x)\big)^2$ is $f(x)$ $f(2x)$ $2f(x)$ None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
235
views
isi2016-dcg
linear-algebra
matrix
1
vote
1
answer
130
ISI2016-DCG-11
Let two systems of linear equations be defined as follows: $\begin{array}{lll} & x+y & =1 \\ P: & 3x+3y & =3 \\ & 5x+5y & =5 \end{array}$ ... $P$ and $Q$ are inconsistent $P$ and $Q$ are consistent $P$ is consistent but $Q$ is inconsistent None of the above
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
243
views
isi2016-dcg
linear-algebra
system-of-equations
1
vote
1
answer
131
ISI2016-DCG-22
The value of $\:\:\begin{vmatrix} 1&\log_{x}y &\log_{x}z \\ \log_{y}x &1 &\log_{y}z \\\log_{z}x & \log_{z}y&1 \end{vmatrix}\:\:$ is $0$ $1$ $-1$ None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
209
views
isi2016-dcg
linear-algebra
determinant
1
vote
1
answer
132
ISI2016-DCG-31
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ stands for determinant of matrix $A.$ Then $\mid\:(A)\mid=1$ $\mid\:(A)\mid=0\:\text{or}\:1$ $\mid\:(A)\mid=-1,0\:\text{or}\:1$ $\mid\:(A)\mid=-1\:\text{or}\:1$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
221
views
isi2016-dcg
linear-algebra
matrix
determinant
0
votes
0
answers
133
ISI2016-DCG-32
The set of vectors constituting an orthogonal basis in $\mathbb{R}^{3}$ is $\begin{Bmatrix} \begin{pmatrix} 1\\ -1 \\0 \end{pmatrix}&,\begin{pmatrix} 1\\ 1 \\0 \end{pmatrix}&,\begin{pmatrix} 0\\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
157
views
isi2016-dcg
linear-algebra
matrix
orthogonal-matrix
eigen-vectors
0
votes
0
answers
134
ISI2016-DCG-33
Suppose $A$ and $B$ are orthogonal $n\times n$ matrices. Which of the following is also an orthogonal matrix? Assume that $O$ is the null matrix of order $n\times n$ and $I$ is the identity matrix of order $n.$ $AB-BA$ $\begin{pmatrix} A & O \\ O & B \end{pmatrix}$ $\begin{pmatrix} A & I \\ I & B \end{pmatrix}$ $A^{2}-B^{2}$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
150
views
isi2016-dcg
linear-algebra
matrix
orthogonal-matrix
0
votes
0
answers
135
ISI2016-DCG-34
Let $A_{ij}$ denote the minors of an $n\times n$ matrix $A.$ What is the relationship between $\mid A_{ij}\mid$ and $\mid A_{ji}\mid$? They are always equal. $\mid A_{ij}\mid=-\mid A_{ji}\mid$ if $i\neq j.$ They are equal if $A$ is a symmetric matrix. If $\mid A_{ij}\mid=0$ then $\mid A_{ji}\mid=0.$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
175
views
isi2016-dcg
linear-algebra
matrix
minors
1
vote
1
answer
136
ISI2017-DCG-4
If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +A-I= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is $A$ $O$ $I$ none of these
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
248
views
isi2017-dcg
linear-algebra
matrix
2
votes
2
answers
137
ISI2017-DCG-7
If $\begin{vmatrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{vmatrix} = k(10!)(11!)(12!)$, then the value of $k$ is $1$ $2$ $3$ $4$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
281
views
isi2017-dcg
linear-algebra
determinant
0
votes
1
answer
138
ISI2017-DCG-25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
284
views
isi2017-dcg
linear-algebra
determinant
definite-integral
non-gate
2
votes
2
answers
139
ISI2018-DCG-16
Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{-1}$ does not exist if $(a,b)$ is equal to $(1,-1)$ $(1,0)$ $(-1,-1)$ $(0,1)$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
316
views
isi2018-dcg
linear-algebra
matrix
inverse
0
votes
0
answers
140
KPGCET-CSE-2019-16
The matrices represented for transformations in homogeneous co-ordinate system are used to transform Multiplication into addition Addition into multiplication Division into subtraction Subtraction into division
gatecse
asked
in
Linear Algebra
Aug 4, 2019
by
gatecse
97
views
kpgcet-cse-2019
engineering-mathematics
linear-algebra
0
votes
0
answers
141
KPGCET-CSE-2019-25
The concatenation of three or more matrices is Associative and also commutative Associative but not commutative Commutative but not associative Neither associative nor commutative
gatecse
asked
in
Linear Algebra
Aug 4, 2019
by
gatecse
165
views
kpgcet-cse-2019
engineering-mathematics
linear-algebra
0
votes
1
answer
142
Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.
Debargha Bhattacharj
asked
in
Linear Algebra
Jun 6, 2019
by
Debargha Bhattacharj
395
views
linear-algebra
0
votes
0
answers
143
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
Hirak
asked
in
Linear Algebra
May 28, 2019
by
Hirak
310
views
eigen-value
linear-algebra
0
votes
1
answer
144
Self-Doubt: Diagonalizable Matrix
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?
srestha
asked
in
Linear Algebra
May 27, 2019
by
srestha
781
views
engineering-mathematics
linear-algebra
matrix
0
votes
1
answer
145
Self Doubt-LA
In a non-homogeneous equation Ax = b, x has a unique solution when $A^{-1}$ exists i.e x = $A^{-1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?
mrinmoyh
asked
in
Mathematical Logic
May 26, 2019
by
mrinmoyh
292
views
linear-algebra
system-of-equations
6
votes
0
answers
146
IISc CSA - Research Interview Question
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$
ankitgupta.1729
asked
in
Graph Theory
May 22, 2019
by
ankitgupta.1729
464
views
graph-theory
linear-algebra
1
vote
1
answer
147
ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
akash.dinkar12
asked
in
Linear Algebra
May 12, 2019
by
akash.dinkar12
357
views
isi2018-pcb-a
engineering-mathematics
linear-algebra
matrix
descriptive
0
votes
1
answer
148
ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
1.2k
views
isi2018-mma
engineering-mathematics
linear-algebra
eigen-value
determinant
1
vote
2
answers
149
ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
644
views
isi2018-mma
engineering-mathematics
linear-algebra
determinant
2
votes
3
answers
150
ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
akash.dinkar12
asked
in
Linear Algebra
May 11, 2019
by
akash.dinkar12
1.1k
views
isi2018-mma
engineering-mathematics
linear-algebra
rank-of-matrix
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Recent questions tagged linear-algebra
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