The determination of the matrix $$$\left[ {\matrix{ 6 & { - 8} & 1 & 1 \cr 0 & 2 & 4 & 6 \cr 0 & 0 & 4 & 8 \cr 0 & 0 & 0 & { - 1} \cr } } \right]\,\,is$$$

Let $$A = ({a_{ij}})$$ be and n-rowed square matrix and $${I_{12}}$$ be the matrix obtained by interchanging the first and second rows of the n-rowed Identity matrix. Then$${AI_{12}}$$ is such that its first

What is the maximum value of the function
$$f\left( x \right) = 2{x^2} - 2x + 6$$ in the interval $$\left[ {0,2} \right]$$?

Each process P_i,i=1.....9 is coded as follows

  Repeat
  P(mutex){
  critical section
  }
  V(mutex)
  Forever

The code for P₁₀ is identical except that it uses V(mutex) in place of P(mutex). What is the largest number of processes that can be inside the critical section at any moment?