If the singular values of a matrix A∈R3×5 are 6, 4, and 1, find ∥A+∥2 and ∥A+∥F.

Answer 1

In the first bit I think you're asking for the (spectral) norm of the matrix, which will be the largest singular value, which 6.

The second part is the Frobenius norm of the matrix, which is the square root of the sum of the square of the singular values, hence sqrt(36+16+1)=sqrt(53).