Vectorize Matrix Formation & Multiplication

How can I vectorize the following code

clear;clc

t = 1:10;
v = rand(10,3);
a = rand(10,1);

m = 6:15;
n = 6:15;

M = 1:20;
N = 1:20;
P = ones(20,20);

V = zeros(size(v))';
D = zeros(size(m))';

for i = 1:length(t)
   
    B = [1,0,0;0,cos(a(i)),sin(a(i));0,-sin(a(i)),cos(a(i))];
    
    V(:,i) = B*v(i,:).';
    
    D(i,1) = interp2(M,N,P,m(i),n(i));
    
end

V = V.'; % (size has to be same as v)

how can I rewrite this code without using loops?

Answer 1

[Matt J]

    N=length(t);
 
     a=reshape(a,1,1,N);

     B=zeros(3,3,N) ;
     B(1,1,:)=1;
     B(2:3,2:3,:)=[cos(a), sin(a); -sin(a),cos(a)];
     
     
    V = pagemtimes(B,reshape(v',2,1,N));
    V=reshape(V,2,[]).';
    
    D = interp2(M,N,P,m,n);

[Fawad Khan]

thank you. this works indeed

although, a minor correction may be

    V = pagemtimes(B,reshape(v',3,1,N));
    V=reshape(V,3,[]).';
    

as v has 3 columns instead of 2