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Recent questions tagged linear-algebra
24
votes
2
answers
781
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
1
vote
1
answer
782
GATE CSE 1993 | Question: 02.3
If the linear velocity $\vec V$ is given by $\vec V = x^2y\,\hat i + xyz\,\hat j – yz^2\,\hat k$ The angular velocity $\vec \omega$ at the point $(1, 1, -1)$ is ________
Kathleen
asked
in
Linear Algebra
Sep 13, 2014
by
Kathleen
1.4k
views
gate1993
linear-algebra
normal
vector-space
out-of-gate-syllabus
fill-in-the-blanks
49
votes
7
answers
783
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
Kathleen
asked
in
Linear Algebra
Sep 13, 2014
by
Kathleen
11.5k
views
gate1993
eigen-value
linear-algebra
easy
multiple-selects
31
votes
3
answers
784
GATE CSE 2008 | Question: 28
How many of the following matrices have an eigenvalue 1? $\left[\begin{array}{cc}1 & 0 \\0 & 0 \end{array} \right]\left[\begin{array}{cc}0 & 1 \\0 & 0 \end{array} \right] \left[\begin{array}{cc}1 & -1 \\1 & 1 \end{array} \right]$ and $\left[\begin{array}{cc}-1 & 0 \\1 & -1 \end{array} \right]$ one two three four
Kathleen
asked
in
Linear Algebra
Sep 11, 2014
by
Kathleen
8.5k
views
gatecse-2008
eigen-value
linear-algebra
29
votes
6
answers
785
GATE CSE 2008 | Question: 3
The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $-1$ any real number
Kathleen
asked
in
Linear Algebra
Sep 11, 2014
by
Kathleen
10.0k
views
gatecse-2008
easy
linear-algebra
system-of-equations
79
votes
5
answers
786
GATE CSE 2007 | Question: 25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$
priya
asked
in
Linear Algebra
Sep 2, 2014
by
priya
16.6k
views
gatecse-2007
eigen-value
linear-algebra
difficult
32
votes
5
answers
787
GATE CSE 2012 | Question: 11
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
gatecse
asked
in
Linear Algebra
Aug 5, 2014
by
gatecse
11.2k
views
gatecse-2012
linear-algebra
eigen-value
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