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TIFRGS2021 Question
Let $M$ be a $n\times m$ real matrix. Consider the following: Let $k_1$ be the smallest number such that $M$ can be factorized as $A.B$, where $A$ is an $n\times k_1$ matrix and $B$ is a $k_1\times m$ matrix. Let $k_2$ ... $k_2 = k_3 < k_1$ (D) $k_1 = k_2 = k_3$ (E) No general relationship exists among $k_1$, $k_2$ and $k_3$
asked
Mar 24
in
Linear Algebra
by
zxy123
(
3.6k
points)

5
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tifr2021
matrices
0
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0
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Finding the transitive closure by using Warshall Algorithm
asked
Nov 1, 2020
in
Set Theory & Algebra
by
Moon_99
(
5
points)

28
views
relations
matrices
0
votes
0
answers
GATE201826 Video Solution
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

14
views
gate2018
linearalgebra
matrices
eigenvalue
normal
videosolution
0
votes
0
answers
GATE200426 Video Solution
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2  n\right)}{2}\right)$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

10
views
gate2004
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE2015118 Video Solution
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

9
views
gate20151
linearalgebra
matrices
numericalanswers
videosolution
0
votes
0
answers
GATE200427 Video Solution
Let $A, B, C, D$ be $n \times n$ matrices, each with nonzero determinant. If $ABCD = I$, then $B^{1}$ is $D^{1}C^{1}A^{1}$ $CDA$ $ADC$ Does not necessarily exist
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

7
views
gate2004
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE200476 Video Solution
In an $M \times N$ matrix all nonzero entries are covered in $a$ rows and $b$ columns. Then the maximum number of nonzero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(Ma, Nb)$ $\leq \min(a, b)$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

9
views
gate2004
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE200623 Video Solution
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

7
views
gate2006
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE2004IT32 Video Solution
Let $A$ be an $n \times n$ ...
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

5
views
gate2004it
linearalgebra
matrices
normal
videosolution
0
votes
0
answers
GATE2008IT29 Video Solution
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

7
views
gate2008it
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE2015227 Video Solution
Perform the following operations on the matrix $\begin{bmatrix} 3 & 4 & 45 \\ 7 & 9 & 105 \\ 13 & 2 & 195 \end{bmatrix}$ Add the third row to the second row Subtract the third column from the first column. The determinant of the resultant matrix is _____.
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

6
views
gate20152
linearalgebra
matrices
easy
numericalanswers
videosolution
0
votes
0
answers
GATE19982.1 Video Solution
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$ $3$ $1$ $2$ $4$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

9
views
gate1998
linearalgebra
matrices
normal
videosolution
0
votes
0
answers
GATE19982.2 Video Solution
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$ Which of the following is a factor of $\Delta$? $a+b$ $ab$ $a+b+c$ $abc$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

10
views
gate1998
linearalgebra
matrices
normal
videosolution
0
votes
0
answers
GATE20011.1 Video Solution
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be nonsingular S2: The sum of two $n \times n$ nonsingular matrices may be singular Which one of the following statements is correct? $S1$ and $S2$ both are true $S1$ is true, $S2$ is false $S1$ is false, $S2$ is true $S1$ and $S2$ both are false
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

3
views
gate2001
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE19941.2 Video Solution
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true? $AA'=I$ $A=A^{1}$ $AB=BA$ $(AB)'=BA$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

16
views
gate1994
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE199302.7 Video Solution
If $A = \begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & i & i \\ 0 & 0 & 0 & i \end{pmatrix}$ the matrix $A^4$, calculated by the use of CayleyHamilton theorem or otherwise, is ____
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

7
views
gate1993
linearalgebra
normal
matrices
numericalanswers
videosolution
0
votes
0
answers
GATE19871xxiii Video Solution
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

20
views
gate1987
linearalgebra
matrices
videosolution
0
votes
0
answers
GATE19951.24 Video Solution
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

6
views
gate1995
linearalgebra
matrices
normal
videosolution
0
votes
0
answers
GATE19943.12 Video Solution
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ 1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

3
views
gate1994
linearalgebra
matrices
easy
descriptive
videosolution
0
votes
0
answers
GATE2004IT36 Video Solution
If matrix $X = \begin{bmatrix} a & 1 \\ a^2+a1 & 1a \end{bmatrix}$ and $X^2  X + I = O$ ($I$ is the identity matrix and $O$ is the zero matrix), then the inverse of $X$ is $\begin{bmatrix} 1a &1 \\ a^2& a \end{bmatrix}$ ... $\begin{bmatrix} a &1 \\ a^2+a1& 1a \end{bmatrix}$ $\begin{bmatrix} a^2a+1 &a \\ 1& 1a \end{bmatrix}$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

9
views
gate2004it
linearalgebra
matrices
normal
videosolution
0
votes
0
answers
GATE19962.6 Video Solution
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 multiplication if $a=b \text{ or } \theta = n\pi, n$ an integer always never if $a \cos\theta = b \sin\theta$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

5
views
gate1996
linearalgebra
normal
matrices
videosolution
0
votes
0
answers
GATE19974.2 Video Solution
Let $A=(a_{ij})$ be an $n$rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$rowed Identify matrix. Then $AI_{12}$ is such that its first Row is the same as its second row Row is the same as the second row of $A$ Column is the same as the second column of $A$ Row is all zero
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

7
views
gate1997
linearalgebra
easy
matrices
videosolution
0
votes
0
answers
GATE19941.9 Video Solution
The rank of matrix $\begin{bmatrix} 0 & 0 & 3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is: $0$ $1$ $2$ $3$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

7
views
gate1994
linearalgebra
matrices
easy
videosolution
0
votes
0
answers
GATE20021.1 Video Solution
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

5
views
gate2002
linearalgebra
easy
matrices
videosolution
0
votes
0
answers
GATE2020CS27 Video Solution
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
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

8
views
gate2020cs
discretemathematics
engineeringmathematics
matrices
videosolution
0
votes
0
answers
GATE199610 Video Solution
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two matrices such that $AB=I$ ... $CD =I$. Express the elements of $D$ in terms of the elements of $B$.
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

3
views
gate1996
linearalgebra
matrices
normal
descriptive
videosolution
0
votes
0
answers
GATE198816i Video Solution
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lowertriangular with all diagonal elements equal to 1, $U$ is uppertriangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
asked
Apr 18, 2020
in
Linear Algebra
by
admin
(
573
points)

8
views
gate1988
normal
descriptive
linearalgebra
matrices
videosolution
0
votes
0
answers
12. Array Ace Academy Booklet
Store only the lower diagonal of $\textbf{Symmetric Square Band Matrix}\;\mathrm{ N\times N}$ in the style of diagonal by diagonal, starting from the lowest diagonal, including main diagonal then calculate the retriveing formula (Assume that ... to solve these questions through a proper procedure which I don't know but looking to learn from the community. Thanks.
asked
Dec 22, 2019
in
Programming
by
`JEET
(
187
points)

64
views
arrays
matrices
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