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GATE CE 2022 Set 2 — Question 30

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NAT+1 / -0MediumMatrix Algebra & OperationsLinear AlgebraEngineering MathematicsEigenvalues & Eigenvectors

Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors

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The components of pure shear strain in a sheared material are given in the matrix form:ε=[111−1]\boldsymbol{\varepsilon} = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}Here, Trace(ε)=0\text{Trace}(\boldsymbol{\varepsilon}) = 0. Given, P=Trace(ε8)P = \text{Trace}(\boldsymbol{\varepsilon}^8) and Q=Trace(ε11)Q = \text{Trace}(\boldsymbol{\varepsilon}^{11}).
The numerical value of (P+Q)(P + Q) is ________. (in integer)
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