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GATE ECE 2011 | Question: 35
The system of equations $$ \begin{aligned} &x+y+z=6 \\ &x+4 y+6 z=20 \\ &x+4 y+\lambda z=\mu \end{aligned} $$ has NO solution for values of $\lambda$ and $\mu$ given by$\...
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695
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GATE ECE 2022 | Question: 2
Consider a system of linear equations $Ax = b,$ where$A =\begin{bmatrix} 1 & – \sqrt{2} & 3 \\ – 1 & \sqrt{2} & – 3 \end{bmatrix}, \quad b = \begin{bmatrix} 1 \\ 3 \end{b...
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1 1 vote
1 1 answer
842
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GATE ECE 2022 | Question: 27
Let $\alpha, \beta$ be two non-zero real numbers and $v_{1}, v_{2}$ be two non-zero real vectors of size $3 \times 1.$ Suppose that $v_{1}$ and $v_{2}$ satisfy $v_{1}^{T}...
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647
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GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular matrix $A$ with repeated eigenvalue is given as$$A=\begin{bmatrix} x & -3.0\\ 3.0 & 4.0 \end{bmatrix}$$where $x$ is a real positive number....
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1 1 vote
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470
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GATE ECE 2020 | Question: 26
Consider the following system of linear equations.$\begin{array}{llll} x_{1}+2x_{2}=b_{1} ; & 2x_{1}+4x_{2}=b_{2}; & 3x_{1}+7x_{2}=b_{3} ; & 3x_{1}+9x_{2}=b_{4} \end{ar...
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GATE ECE 2019 | Question: 17
The number of distinct eigenvalues of the matrix$$A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$$is equal to ____________.
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3.1k
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GATE ECE 2016 Set 3 | Question: 1
Consider a $2\times2$ sqaure matrix $$\textbf{A}= \begin{bmatrix} \sigma &x\\ \omega &\sigma \end{bmatrix},$$ where $x$ is unknown. If the eigen values of the matrix $\te...
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515
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GATE ECE 2016 Set 2 | Question: 1
The value of $x$ for which the matrix $A= \begin{bmatrix} 3& 2 &4 \\ 9& 7 & 13\\ -6&-4 &-9+x \end{bmatrix}$ has zero as an eigenvalue is ________
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482
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GATE ECE 2016 Set 2 | Question: 29
The matrix $A=\begin{bmatrix} a & 0 &3 &7 \\ 2& 5&1 &3 \\ 0& 0& 2 &4 \\ 0&0 & 0 &b \end{bmatrix}$ has $\text{det}(A) = 100$ and $\text{trace}(A) = 14$. The value of $\mid...
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524
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GATE ECE 2016 Set 1 | Question: 1
Let $M^4$= $I$,(where $I$ denotes the identity matrix) and $ M \neq I$, $M^2\neq I$ and $M^3\neq I$. Then,for any natural number $k$, $M^{-1}$ equals:$M^{4k+1}$ $M^{4...
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593
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GATE ECE 2016 Set 1 | Question: 27
A sequence $x[n]$ is specified as $\begin{bmatrix}x[n] \\x[n – 1]\end{bmatrix}=\begin{bmatrix}1&1\\1&0\end{bmatrix}^n\begin{bmatrix}1\\0\end{bmatrix}$,for $n \geq 2$.The ...
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471
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GATE ECE 2015 Set 3 | Question: 1
For $A = \begin{bmatrix} 1 &\tan x \\ -\tan x &1 \end{bmatrix},$ the determinant of $A^{T}A^{-1}$ is$\sec^{2}x$$\cos 4x$$1$$0$
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466
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GATE ECE 2015 Set 2 | Question: 2
The value of $x$ for which all the eigen-values of the matrix given below are real is $$\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &-10 \end{bmatrix}$$$5+j$$5-j$$1-5j$$1...
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387
387 views
GATE ECE 2015 Set 2 | Question: 46
The state variable representation of a system is given as$\dot{x} = \begin{bmatrix} 0 &1 \\ 0 &-1 \end{bmatrix}\: ; x(0)=\begin{bmatrix} 1\\0 \end{bmatrix}$$y=\begin{bm...
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449
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GATE ECE 2015 Set 1 | Question: 1
Consider a system of linear equations:$$x-2y+3z=-1, \\ x-3y+4z=1, \text{ and } \\ -2x+4y-6z=k.$$ The value of $k$ for which the system has infinitely many solutions is __...
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1 1 answer
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GATE ECE 2015 Set 1 | Question: 5
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigenvector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 ...
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434
434 views
GATE ECE 2015 Set 1 | Question: 43
Two sequences $\begin{bmatrix}a, & b, & c \end{bmatrix}$ and $\begin{bmatrix}A, & B, & C \end{bmatrix}$ are related as,$$\begin{bmatrix}A \\ B \\ C \end{bmatrix} = \be...
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375
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GATE ECE 2014 Set 4 | Question: 46
The state transition matrix $\phi(t)$ of a system $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \...
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535
535 views
GATE ECE 2014 Set 3 | Question: 27
Which one of the following statements is NOT true for a square matrix $A$?If $A$ is upper triangular, the eigenvalues of $A$ are the diagonal elements of itIf $A$ is real...
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493
493 views
GATE ECE 2014 Set 3 | Question: 47
The state equation of a second-order linear system is given by$$\dot{x}(t)=Ax(t), \:\:\:\:\:\:\:\:x(0)=x_{0}$$For $x_{0}= \begin{bmatrix} 1\\ -1 \end{bmatrix},$ $x(t)...
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