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Recent questions tagged matrices

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GATE Mechanical 2021 Set 2 | Question: 1
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1...
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GATE Mechanical 2021 Set 2 | Question: 27
Let the superscript $\text{T}$ represent the transpose operation. Consider the function $f(x)=\frac{1}{2}x^TQx-r^Tx$, where $x$ and $r$ are $n \times 1$ vectors and $\tex...
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GATE2020-ME-2: 2
A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$. If $$S= \begin{pmatrix} -4 & 4 & 2 \\ 4 & 3 & 7/2 \\ 2 & 7/2 & 2 \end{pmatrix}, \: \: ...
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GATE2020-ME-1: 1
Multiplication of real valued square matrices of same dimension isassociativecommutativealways positive definitenot always possible to compute
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GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$,$[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{...
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GATE2019 ME-1: 1
Consider the matrix$$P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$$The number of distinct eigenvalues$0$$1$$2$$3$
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GATE2018-2-19
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).
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262
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GATE2018-1-2
The rank of the matrix $\begin{bmatrix} -4 & 1 & -1 \\ -1 & -1 & -1 \\ 7 & -3 & 1 \end{bmatrix}$ is$1$$2$$3$$4$
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GATE2017 ME-2: 3
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
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GATE2017 ME-1: 26
Consider the matrix $P=\begin{bmatrix} \dfrac{1}{\sqrt{2}} & 0 &\dfrac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ -\dfrac{1}{\sqrt{2}} &0 & \dfrac{1}{\sqrt{2}}\end{bmatrix}$ Which one ...
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348
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GATE2017 ME-1: 1
The product of eigenvalues of the matrix $P$ is$P=\begin{bmatrix}2 & 0 & 1\\ 4& -3 &3 \\ 0 & 2 & -1\end{bmatrix}$$-6$$2$$6$$-2$
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GATE2016-3-1
A real square matrix $\textbf{A}$ is called skew-symmetric if$A^T=A$$A^T=A^{-1}$$A^T=-A$$A^T=A+A^{-1}$
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209
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GATE2016-2-1
The condition for which the eigenvalues of the matrix$A=\begin{bmatrix} 2 & 1\\ 1 & k \end{bmatrix}$are positive, is$k 1/2$$k −2$$k 0$$k < −1/2$
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219
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GATE2016-1-1
The solution to the system of equations$\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is$6,2$$-6,2$$...
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274
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GATE2015-3-42
For a given matrix $P=\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix}$, where $i=\sqrt{-1}$, the inverse of matrix $P$ is$P=\displaystyle{\frac{1}{24}}\begin{bmatrix} ...
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261
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GATE2015-3-15
The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________
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GATE2015-2-1
At least one eigenvalue of a singular matrix ispositivezeronegativeimaginary
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GATE2015-1-1
If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding ...
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GATE Mechanical 2014 Set 4 | Question: 1
Which one of the following equations is a correct identity for arbitrary $3 \times 3$ real matrices $P$, $Q$ and $R$?$P(Q+R)=PQ+RP$$(P-Q)^2 = P^2 -2PQ -Q^2$$\text{det } ...
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354
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GATE Mechanical 2014 Set 3 | Question: 1
Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmat...
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GATE Mechanical 2014 Set 1 | Question: 1
Given that the determinant of the matrix $\begin{bmatrix} 1 & 3 & 0\\ 2 & 6 & 4\\ -1 & 0 & 2 \end{bmatrix}$ is $-12$, the determinant of the matrix $\begin{bmatrix} 2 & 6...
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GATE Mechanical 2014 Set 1 | Question: 4
The matrix form of the linear syatem $\dfrac{dx}{dt}=3x-5y$ and $\dfrac{dy}{dt}=4x+8y$ is$\dfrac{d}{dt}\begin{Bmatrix} x\\y \end{Bmatrix}=\begin{bmatrix} 3 & -5\\ 4& 8 \e...
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GATE ME 2013 | Question: 2
The eigen values of a symmetric matrix are allcomplex with non-zero positive imaginary part.complex with non-zero negative imaginary part.real.pure imaginary.
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