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Webpage for Linear Algebra
Recent questions tagged linear-algebra
1
votes
1
answer
391
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 $\mid\:(A)\mid=1$ $\mid\:(A)\mid=0\:\text{or}\:1$ $\mid\:(A)\mid=-1,0\:\text{or}\:1$ $\mid\:(A)\mid=-1\:\text{or}\:1$
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}\...
gatecse
385
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2016-dcg
linear-algebra
matrix
determinant
+
–
0
votes
0
answers
392
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
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{pmatri...
gatecse
316
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2016-dcg
linear-algebra
matrix
orthogonal-matrix
eigen-vectors
+
–
0
votes
0
answers
393
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}$
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 ...
gatecse
260
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2016-dcg
linear-algebra
matrix
orthogonal-matrix
+
–
0
votes
0
answers
394
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.$
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}\...
gatecse
295
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2016-dcg
linear-algebra
matrix
minors
+
–
1
votes
1
answer
395
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
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$$I$none of ...
gatecse
445
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2017-dcg
linear-algebra
matrix
+
–
2
votes
2
answers
396
ISI2017-DCG-7
If $\begin{vmatrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{vmatrix} = k(10!)(11!)(12!)$, then the value of $k$ is $1$ $2$ $3$ $4$
If $\begin{vmatrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{vmatrix} = k(10!)(11!)(12!)$, then the value of $k$ is$1$$2$$3$$4$
gatecse
537
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2017-dcg
linear-algebra
determinant
+
–
1
votes
1
answer
397
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 $\pi$ $\frac{\pi}{2}$ $0$ $1$
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}} [...
gatecse
585
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2017-dcg
linear-algebra
determinant
definite-integral
non-gate
+
–
2
votes
2
answers
398
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 $(1,-1)$ $(1,0)$ $(-1,-1)$ $(0,1)$
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
512
views
gatecse
asked
Sep 18, 2019
Linear Algebra
isi2018-dcg
linear-algebra
matrix
inverse
+
–
0
votes
0
answers
399
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
The matrices represented for transformations in homogeneous co-ordinate system are used to transformMultiplication into additionAddition into multiplicationDivision into ...
gatecse
182
views
gatecse
asked
Aug 4, 2019
Linear Algebra
kpgcet-cse-2019
engineering-mathematics
linear-algebra
+
–
0
votes
0
answers
400
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
The concatenation of three or more matrices isAssociative and also commutativeAssociative but not commutative Commutative but not associativeNeither associative nor commu...
gatecse
220
views
gatecse
asked
Aug 4, 2019
Linear Algebra
kpgcet-cse-2019
engineering-mathematics
linear-algebra
+
–
0
votes
1
answer
401
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$.
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 s...
Debargha Bhattacharj
681
views
Debargha Bhattacharj
asked
Jun 6, 2019
Linear Algebra
linear-algebra
+
–
0
votes
0
answers
402
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
Hirak
504
views
Hirak
asked
May 28, 2019
Linear Algebra
eigen-value
linear-algebra
+
–
0
votes
1
answer
403
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?
$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 diagona...
srestha
1.3k
views
srestha
asked
May 27, 2019
Linear Algebra
engineering-mathematics
linear-algebra
matrix
+
–
0
votes
1
answer
404
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?
In a non-homogeneous equation Ax = b, x has a unique solution when $A^{-1}$ exists i.e x = $A^{-1}$bbut when det(A) = 0 then we have infinite solution or many solution.p...
mrinmoyh
471
views
mrinmoyh
asked
May 26, 2019
Mathematical Logic
linear-algebra
system-of-equations
+
–
6
votes
0
answers
405
IISc CSA - Research Interview Question
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$
ankitgupta.1729
676
views
ankitgupta.1729
asked
May 22, 2019
Graph Theory
graph-theory
linear-algebra
+
–
1
votes
1
answer
406
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$.
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\alp...
akash.dinkar12
519
views
akash.dinkar12
asked
May 12, 2019
Linear Algebra
isi2018-pcb-a
engineering-mathematics
linear-algebra
matrix
descriptive
+
–
0
votes
1
answer
407
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$
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
1.7k
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
eigen-value
determinant
+
–
1
votes
2
answers
408
ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is$2$$2(1+i)$$0$$2^{10}$
akash.dinkar12
914
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
determinant
+
–
3
votes
4
answers
409
ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
The rank of the matrix$\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$$1$$2$$3$$4$
akash.dinkar12
1.5k
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
rank-of-matrix
+
–
1
votes
1
answer
410
ISI2018-MMA-11
The value of $\lambda$ for which the system of linear equations $2x-y-z=12$, $x-2y+z=-4$ and $x+y+\lambda z=4$ has no solution is $2$ $-2$ $3$ $-3$
The value of $\lambda$ for which the system of linear equations $2x-y-z=12$, $x-2y+z=-4$ and $x+y+\lambda z=4$ has no solution is$2$$-2$$3$$-3$
akash.dinkar12
884
views
akash.dinkar12
asked
May 11, 2019
Quantitative Aptitude
isi2018-mma
engineering-mathematics
linear-algebra
system-of-equations
+
–
1
votes
1
answer
411
ISI2019-MMA-23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skew-symmetric matrix None of the above must necessarily hold
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, the...
Sayan Bose
1.7k
views
Sayan Bose
asked
May 7, 2019
Linear Algebra
isi2019-mma
engineering-mathematics
linear-algebra
matrix
+
–
1
votes
2
answers
412
ISI2019-MMA-15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$$2$ for any real number $t$$2$ or $3$ depending o...
Sayan Bose
1.4k
views
Sayan Bose
asked
May 6, 2019
Linear Algebra
isi2019-mma
linear-algebra
engineering-mathematics
matrix
+
–
2
votes
1
answer
413
ISI2019-MMA-14
If the system of equations $\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$
If the system of equations$\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$with $a,b,c \neq 1$ has a non trivial solutions, the value of $$\frac{1}{...
Sayan Bose
960
views
Sayan Bose
asked
May 6, 2019
Linear Algebra
isi2019-mma
linear-algebra
system-of-equations
+
–
1
votes
2
answers
414
ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is$8$$10$$12$$1...
Sayan Bose
2.3k
views
Sayan Bose
asked
May 6, 2019
Linear Algebra
isi2019-mma
engineering-mathematics
linear-algebra
vector-space
non-gate
+
–
0
votes
0
answers
415
CSIR UGC NET
Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. Then Both $A$ and $A^2+3 A$ are invertible $A^2+3 A$ is invertible but $A$ is not invertible $A$ is invertible but $A^2+3 A$ is not invertible Both $\mathrm{A}$ and $A^2+3 A$ are not invertible.
Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. ThenBoth $A$ and $A^2+3 A...
Hirak
567
views
Hirak
asked
Apr 28, 2019
Linear Algebra
linear-algebra
eigen-value
matrix
+
–
4
votes
1
answer
416
Vani Institute Question Bank Pg-231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______$a,a,a$$0,a,2a$$-a,2a,2a$$a,a+\sqrt{2},a-\sqrt{2}$
Hirak
1.3k
views
Hirak
asked
Apr 25, 2019
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
27
votes
7
answers
417
GATE CSE 2019 | Question: 9
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is non-zero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
Let $X$ be a square matrix. Consider the following two statements on $X$.$X$ is invertibleDeterminant of $X$ is non-zeroWhich one of the following is TRUE?I implies II; I...
Arjun
10.6k
views
Arjun
asked
Feb 7, 2019
Linear Algebra
gatecse-2019
engineering-mathematics
linear-algebra
determinant
1-mark
+
–
26
votes
4
answers
418
GATE CSE 2019 | Question: 44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
Consider the following matrix:$R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$The absolute value of the product ...
Arjun
19.6k
views
Arjun
asked
Feb 7, 2019
Linear Algebra
gatecse-2019
numerical-answers
engineering-mathematics
linear-algebra
eigen-value
2-marks
+
–
4
votes
2
answers
419
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix But how to calculate value of x when nullity is already given(1 in this case)
Nullity of a matrix = Total number columns – Rank of that matrixBut how to calculate value of x when nullity is already given(1 in this case)
Nandkishor3939
3.4k
views
Nandkishor3939
asked
Jan 24, 2019
Linear Algebra
engineering-mathematics
linear-algebra
matrix
rank-of-matrix
+
–
0
votes
1
answer
420
Simple Determinant
how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??
how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??
BHASHKAR
302
views
BHASHKAR
asked
Jan 19, 2019
Linear Algebra
linear-algebra
engineering-mathematics
matrix
+
–
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