If the system of linear equations

2x + y $$-$$ z = 7

x $$-$$ 3y + 2z = 1

x + 4y + $$\delta$$z = k, where $$\delta$$, k $$\in$$ R has infinitely many solutions, then $$\delta$$ + k is equal to:

Let $$A = [{a_{ij}}]$$ be a square matrix of order 3 such that $${a_{ij}} = {2^{j - i}}$$, for all i, j = 1, 2, 3. Then, the matrix A² + A³ + ...... + A¹⁰ is equal to :

If the system of linear equations

$$2x + 3y - z = - 2$$

$$x + y + z = 4$$

$$x - y + |\lambda |z = 4\lambda - 4$$

where, $$\lambda$$ $$\in$$ R, has no solution, then

Let A be a matrix of order 3 $$\times$$ 3 and det (A) = 2. Then det (det (A) adj (5 adj (A³))) is equal to _____________.