Recent questions tagged matrices - GATE CSE Doubts

0 votes

0 answers

TIFR-GS2021 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 views

0 votes

0 answers

Finding the transitive closure by using Warshall Algorithm

asked Nov 1, 2020 in Set Theory & Algebra by Moon_99 (5 points) | 28 views

0 votes

0 answers

GATE2018-26 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

0 votes

0 answers

GATE2004-26 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

0 votes

0 answers

GATE2015-1-1‏8 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

0 votes

0 answers

GATE2004-27 Video Solution
Let $A, B, C, D$ be $n \times n$ matrices, each with non-zero 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

0 votes

0 answers

GATE2004-76 Video Solution
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$

asked Apr 18, 2020 in Linear Algebra by admin (573 points) | 9 views

0 votes

0 answers

GATE2006-23 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

0 votes

0 answers

GATE2004-IT-32 Video Solution
Let $A$ be an $n \times n$ ...

asked Apr 18, 2020 in Linear Algebra by admin (573 points) | 5 views

0 votes

0 answers

GATE2008-IT-29 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

0 votes

0 answers

GATE2015-2-27 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

0 votes

0 answers

GATE1998-2.1 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

0 votes

0 answers

GATE1998-2.2 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 $\Delta$? $a+b$ $a-b$ $a+b+c$ $abc$

asked Apr 18, 2020 in Linear Algebra by admin (573 points) | 10 views

0 votes

0 answers

GATE2001-1.1 Video Solution
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be non-singular S2: The sum of two $n \times n$ non-singular 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

0 votes

0 answers

GATE1994-1.2 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

0 votes

0 answers

GATE1993-02.7 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 Cayley-Hamilton theorem or otherwise, is ____

asked Apr 18, 2020 in Linear Algebra by admin (573 points) | 7 views

0 votes

0 answers

GATE1987-1-xxiii 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

0 votes

0 answers

GATE1995-1.24 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

0 votes

0 answers

GATE1994-3.12 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

0 votes

0 answers

GATE2004-IT-36 Video Solution
If matrix $X = \begin{bmatrix} a & 1 \\ -a^2+a-1 & 1-a \end{bmatrix}$ and $X^2 - X + I = O$ ($I$ is the identity matrix and $O$ is the zero matrix), then the inverse of $X$ is $\begin{bmatrix} 1-a &-1 \\ a^2& a \end{bmatrix}$ ... $\begin{bmatrix} -a &1 \\ -a^2+a-1& 1-a \end{bmatrix}$ $\begin{bmatrix} a^2-a+1 &a \\ 1& 1-a \end{bmatrix}$

asked Apr 18, 2020 in Linear Algebra by admin (573 points) | 9 views

0 votes

0 answers

GATE1996-2.6 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

0 votes

0 answers

GATE1997-4.2 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

0 votes

0 answers

GATE1994-1.9 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

0 votes

0 answers

GATE2002-1.1 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

0 votes

0 answers

GATE2020-CS-27 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

0 votes

0 answers

GATE1996-10 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

0 votes

0 answers

GATE1988-16i Video Solution
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to 1, $U$ is upper-triangular, 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

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

To see more, click for the full list of questions or popular tags.

9,200 questions

3,182 answers

14,686 comments

96,168 users