Hot questions in Linear Algebra / GO Electrical

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21

GATE Electrical 2013 | Question: 51
The state variable formulation of a system is given as $\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1-\dfrac{1}{2}e^{-2t}-\dfrac{1}{2}e^{-t} \\$ $e^{-2t}-e^{-t} \\$ $1-e^{-t}$

The state variable formulation of a system is given as$\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x...

piyag476

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piyag476 asked Feb 11, 2017

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22

GATE Electrical 2013 | Question: 35
A matrix has eigenvalues $-1$ and $-2$. The corresponding eigenvectors are $\begin{bmatrix} 1\\-1 \end{bmatrix}$ and $\begin{bmatrix} 1\\-2 \end{bmatrix}$ respectibely. The matrix is $\begin{bmatrix} 1 & 1\\ -1 & -2 \end{bmatrix} \\$ ... $\begin{bmatrix} 0& 1\\ -2 & 3 \end{bmatrix}$

A matrix has eigenvalues $–1$ and $–2$. The corresponding eigenvectors are $\begin{bmatrix} 1\\-1 \end{bmatrix}$ and $\begin{bmatrix} 1\\-2 \end{bmatrix}$ respectibel...

piyag476

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piyag476 asked Feb 11, 2017

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23

GATE Electrical 2014 Set 3 | Question: 1
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N – 1$ $N$ $2N$

Two matrices $A$ and $B$ are given below:$A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$If the rank of...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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24

GATE Electrical 2013 | Question: 25
The equation$\begin{bmatrix} 2&-2 \\ 1& -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ has no solution only one solution $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ non-zero unique solution multiple solutions

The equation$\begin{bmatrix} 2&-2 \\ 1& -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ hasno solutiononly one solution $\begi...

piyag476

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piyag476 asked Feb 11, 2017

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25

GATE Electrical 2016 Set 2 | Question: 49
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ corresponding to distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$ respectively. Then the ... $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$

Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ co...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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26

GATE Electrical 2016 Set 2 | Question: 32
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$

Let $P=\begin{bmatrix} 3&1 \\ 1 & 3\end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix}x\\ y\end{pmatrix}$ such that $a^{2}+b^{2}=1$ where $\begin{pmatrix}...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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27

GATE Electrical 2016 Set 1 | GA Question: 5
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$ $n^{4}$ $4^{n}$ $2^{2n-1}$ $4^{n-1}$

In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\dfrac{\alpha^{n}+\beta^{n}}{\alpha^{-n}+\beta^{-n}}$$n^{4}$$4...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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28

GATE Electrical 2016 Set 1 | Question: 2
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.

Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only non-zero eigenvalue is ________.

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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29

GATE Electrical 2016 Set 1 | Question: 28
Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, -2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}-3A+4I$ would, respectively, be $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1} - x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1} - x_{2}$

Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, -2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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30

GATE Electrical 2016 Set 1 | Question: 29
Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE? Rank of $A^{T} A$ is less than $2$. Rank of $A^{T} A$ is equal to $2$. Rank of $A^{T} A$ is greater than $2$. Rank of $A^{T} A$ can be any number between $1$ and $3$.

Let $A$ be a $4 \times 3$ real matrix with rank $2$. Which one of the following statement is TRUE?Rank of $A^{T} A$ is less than $2$.Rank of $A^{T} A$ is equal to $2$.Ran...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017

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31

GATE Electrical 2016 Set 2 | Question: 7
A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$

A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are$1, 1, −1$$1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆...

makhdoom ghaya

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makhdoom ghaya asked Jan 29, 2017