The components of pure shear strain in a sheared are given in the matrix form:

$$\varepsilon = \left[ {\matrix{ 1 & 1 \cr 1 & { - 1} \cr } } \right]$$

Here, Trace ($$\varepsilon $$) = 0. Given, P = Trace ($$\varepsilon$$⁸) and Q = Trace ($$\varepsilon $$¹¹).

The numerical value of (P + Q) is ___________. (in integer)

P and Q are two square matrices of the same order. Which of the following statements is/are correct?

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M³ $$-$$ 4M² $$-$$ 2M

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are