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Recent questions and answers in Linear Algebra
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votes
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GATE2017 ME2: 28
Consider the matrix $A=\begin{bmatrix} 50 &70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{bmatrix} 70 \\ \lambda_{1}50 \end{bmatrix}$ and $x_{2}=\begin{bmatrix} \lambda _{2}80\\ 70 \end{bmatrix}$, respectively. The value of $x^{T}_{1} x_{2}$ is _________.
answered
May 24
in
Linear Algebra
by
ankitgupta.1729
(
390
points)
gate2017me2
0
votes
1
answer
GATE2019 ME2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & 4 \\ 4 & 4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
answered
May 24
in
Linear Algebra
by
ankitgupta.1729
(
390
points)
gate2019me2
0
votes
1
answer
GATE2019 ME1: 1
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
answered
Feb 15
in
Linear Algebra
by
aditya_kr
(
140
points)
gate2019me1
0
votes
1
answer
GATE2018219
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{1})$ is _______ (correct to two decimal palces).
answered
Feb 22, 2018
in
Linear Algebra
by
Balaji Jegan
(
1.2k
points)
gate2018me2
0
votes
0
answers
GATE201812
The rank of the matrix $\begin{bmatrix} 4 & 1 & 1 \\ 1 & 1 & 1 \\ 7 & 3 & 1 \end{bmatrix}$ is 1 2 3 4
asked
Feb 17, 2018
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2018me1
0
votes
1
answer
GATE2017 ME2: 3
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
answered
Feb 14, 2018
in
Linear Algebra
by
m2n037
(
940
points)
gate2017me2
0
votes
0
answers
GATE2017 ME2: 2
The divergence of the vector $yi+xj$ is ________.
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2017me2
0
votes
0
answers
GATE2017 ME2: 1
Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2017me2
0
votes
0
answers
GATE2017 ME2: 4
A sample of $15$ data is as follows: $17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3$. The mode of the data is $4$ $13$ $17$ $20$
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2017me2
0
votes
0
answers
GATE2017 ME1: 26
Consider the matrix $P=\begin{bmatrix} \frac{1}{\sqrt{2}} & 0 &\frac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ \frac{1}{\sqrt{2}} &0 & \frac{1}{\sqrt{2}} \end{bmatrix}$ Which one of the following statements about $P$ is INCORRECT ? Determinant of P is equal to $1$. $P$ is orthogonal. Inverse of $P$ is equal to its transpose. All eigenvalues of $P$ are real numbers.
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2017me1
0
votes
0
answers
GATE2017 ME1: 1
The product of eigenvalues of the matrix $P$ is $P=\begin{bmatrix} 2 & 0 & 1\\ 4& 3 &3 \\ 0 & 2 & 1 \end{bmatrix}$ $6$ $2$ $6$ $2$
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2017me1
0
votes
0
answers
GATE2017 ME1: 3
Consider the following partial differential equation for $u(x, y)$, with the constant $c > 1$: $\frac{\partial u}{\partial y}+c\frac{\partial u}{\partial x}=0$ Solution of this equation is $u(x, y) = f (x+cy)$ $u(x, y) = f (xcy)$ $u(x, y) = f (cx+y)$ $u(x, y) = f (cxy)$
asked
Feb 27, 2017
in
Linear Algebra
by
Arjun
(
21.2k
points)
gate2017me1
0
votes
0
answers
GATE20132
The eigen values of a symmetric matrix are all complex with nonzero positive imaginary part. complex with nonzero negative imaginary part. real. pure imaginary.
asked
Feb 19, 2017
in
Linear Algebra
by
piyag476
(
1.4k
points)
gate2013me
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