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Recent questions tagged matrix
17
votes
3
answers
361
GATE CSE 1994 | Question: 3.12
Find the inverse of the matrix $\begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix}$
Kathleen
asked
in
Linear Algebra
Oct 5, 2014
by
Kathleen
4.6k
views
gate1994
linear-algebra
matrix
easy
descriptive
18
votes
4
answers
362
GATE CSE 1994 | Question: 1.9
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is: $0$ $1$ $2$ $3$
Kathleen
asked
in
Linear Algebra
Oct 4, 2014
by
Kathleen
5.6k
views
gate1994
linear-algebra
matrix
rank-of-matrix
easy
26
votes
3
answers
363
GATE CSE 1994 | Question: 1.2
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true? $AA'=I$ $A=A^{-1}$ $AB=BA$ $(AB)'=BA$
Kathleen
asked
in
Linear Algebra
Oct 4, 2014
by
Kathleen
7.8k
views
gate1994
linear-algebra
normal
matrix
23
votes
7
answers
364
GATE CSE 1997 | Question: 4.2
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 Identity 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
Kathleen
asked
in
Linear Algebra
Sep 29, 2014
by
Kathleen
4.9k
views
gate1997
linear-algebra
easy
matrix
25
votes
5
answers
365
GATE CSE 1998 | Question: 2.2
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 $\Delta$? $a+b$ $a-b$ $a+b+c$ $abc$
Kathleen
asked
in
Linear Algebra
Sep 25, 2014
by
Kathleen
7.3k
views
gate1998
linear-algebra
matrix
normal
20
votes
4
answers
366
GATE CSE 1998 | Question: 2.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$ $3$ $1$ $2$ $4$
Kathleen
asked
in
Linear Algebra
Sep 25, 2014
by
Kathleen
7.0k
views
gate1998
linear-algebra
matrix
normal
rank-of-matrix
35
votes
4
answers
367
GATE CSE 2004 | Question: 76
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 $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$
Kathleen
asked
in
Linear Algebra
Sep 18, 2014
by
Kathleen
9.6k
views
gatecse-2004
linear-algebra
normal
matrix
35
votes
4
answers
368
GATE CSE 2004 | Question: 27
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
Kathleen
asked
in
Linear Algebra
Sep 18, 2014
by
Kathleen
10.0k
views
gatecse-2004
linear-algebra
normal
matrix
25
votes
7
answers
369
GATE CSE 2004 | Question: 26
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 $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2 - n\right)}{2}\right)$
Kathleen
asked
in
Linear Algebra
Sep 18, 2014
by
Kathleen
12.5k
views
gatecse-2004
linear-algebra
normal
matrix
44
votes
5
answers
370
GATE CSE 2006 | Question: 23
$F$ 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
Rucha Shelke
asked
in
Linear Algebra
Sep 17, 2014
by
Rucha Shelke
9.9k
views
gatecse-2006
linear-algebra
normal
matrix
16
votes
3
answers
371
GATE CSE 2002 | Question: 1.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
Kathleen
asked
in
Linear Algebra
Sep 15, 2014
by
Kathleen
4.0k
views
gatecse-2002
linear-algebra
easy
matrix
23
votes
6
answers
372
GATE CSE 2001 | Question: 1.1
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
Kathleen
asked
in
Linear Algebra
Sep 14, 2014
by
Kathleen
8.4k
views
gatecse-2001
linear-algebra
normal
matrix
24
votes
2
answers
373
GATE CSE 1993 | Question: 02.7
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 _______
Kathleen
asked
in
Linear Algebra
Sep 13, 2014
by
Kathleen
5.6k
views
gate1993
linear-algebra
normal
matrix
fill-in-the-blanks
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