Given this 3 x 3 matrix:

define a simple procedure with the minimal number of operations resulting in the value of 682.

you could say that my solution is quite vectorious :-)

let V1 be the row vector {11,0,0}
let V2 be the column vector {31,0,0}
let M be the 3x3 matrix of all 2's
then V1.M.V2 = 682
in fact, if you let V1 = {1,0,0} and V2={N/2,0,0} then
V1.M.V2 = N and thus you can get any result you want in just two multiplications.  Of course, one could argue how to count the operations in this solution.  Is it 2 matrix/vector multiplications, or do you count how many numerical multiplications and additions are needed to complete the calculation?

Posted by Daniel on 2012-04-14 16:38:04