How to do repeated random sample from a matrix

Hi, I am trying to figure out a problem. Suppose I have two matrices,one is parameter matrix B, which is 10,000*11.I obtain B from MVN simulation by 10,000 times. Elements from any row of B is denoted as b0(constant), b1, b2, b3, ...b11. Another matrix is X, an 11*10,000 matrix,The row is the number of observations, and the column is the number of variables. Elements of any column from X is denoted as x1 x2 ...x11.Now I need to randomly select one row from B and one column from X,respectively and then obtain y1= b0+b1*x1+b2*x2+...b11*x11. I need to repeat this process for 10,000 times so that I will obtain a column of 10,000*1 Y(=y1 y2 y3 ...y10,000). Please give me some ideas for this. Thanks!

Answer 1

[Star Strider]

It seems to me that you are doing simple matrix multiplication, then summing across the columns:

Y = sum(B*X,2);

[Tommy Tang]

Yes. I will need to do multiplication. But the difficult part is how to simultaneously select row and column from two matrices and then multiply for 10,000 times.

[Star Strider]

The approach I described does all of the multiplications at once. The original product matrix is (10000 x 10000), so to get your (10000 x 1) vector, I add across the columns. I thought that is what you want to do.