How to solve a [non-]convex problem with multiple scalar and matrix variables

I have a three given matrices Y1(n,m), Y2(n,m) and Y3(n,m) that I would like to approximate to a weighted decomposition where another matrix A(m,k) is given and X(k,n) is unknown such that Y1=aAX, Y2=bAX and Y3=cAX. So I would like to solve the following problem in cvx where I want to find a,b,c and the matrix X:

cvx_begin sdp
    variables a b c X(k,n)
    minimize(norm(Y1-a*A*X) + norm(Y2-b*A*X) + norm(Y3-c*A*X))

But I got the following error: Disciplined convex programming error:
Only scalar quadratic forms can be specified in CVX

I would appreciate any help.

Your problem is not, in fact, convex.