The recurrence relation below is for the time$-$complexity of multiplication of two matrices A

and B using Strassen$$s algorithm. The algorithm partitions each of the matrices into $4$ submatrices

of half the size of the original matrix; it computes $10$ matrix$-$add or $-$subtract operations taking

O$($n

$2$

$),$ and use the results and $4$ submatrices to define seven products. Thus, there are $7$ recursive

calls. The recurrence equation for computation time is given by:

T$($n$)=$

$\backslash$Theta $(1)$ if n $=1$

$7$T$($n$/2)+\backslash$Theta $($n

$2$

$)$ if n $>1$; note a $=7,$ b $=2,$ f$($n$)=$ n

$2$

$(1)$

You don$$t have to know the algorithm, but if you are interested read the Section $4\mathrm{.}2$ of the textbook.