Q$3$ Matrix multiplication $($Divide and Conquer$)$

$4$ Points

Assume someone discovers a way of multiplying $4040$ matrices using $40000$ scalar

multiplications, a way of multiplying $4545$ matrices using $45000$ scalar multiplications, and a

way of multiplying $5050$ matrices using $50000$ scalar multiplications. Which method yields the

best asymptotic running time when used in a divide$-$and$-$conquer matrix$-$multiplication algorithm?

How does it compare to Strassen's algorithm?

Q$3\mathrm{.}11$st $($ best$)$

$1$ Point

The asymptotically fastest method is

The $40-$algorithm

The $45-$algorithm

The $50-$algorithm

Strassen's algorithm

Last saved on Apr $12$ at $6$:$04$ AM

Q$3\mathrm{.}22$nd

$1$ Point

The asymptotically second$-$best method is

The $40-$algorithm

The $45-$algorithm

The $50-$algorithm

Strassen's algorithm

Last saved on Apr $11$ at $6$:$58$ AM

Q$3.33$rd

$1$ Point

The asymptotically third$-$best method is

The $40-$algorithm

The $45-$algorithm

The $50-$algorithm

Strassen's algorithm