Problem $3.$ Write a function that accepts a matrix A and a positive integer $s.$

Use your function from Problem $1$ or scipy.linalg.svd$()$ to compute the compact SVD

of $A,$ then form the truncated SVD by stripping off the appropriate columns and entries

from $U_1,{}_1,$ and $V_1.$ Return the best rank $s$ approximation $A_s$ of $A($with respect to the

induced $2-$norm and Frobenius norm$).$

Also return the number of entries required to store the truncated form widehat$(U)widehat()widehat(V{)}^H($where widehat$()$

is stored as a one$-$dimensional array, not the full diagonal matrix$).$ The number of entries

stored in NumPy array can be accessed by its size attribute.

If $s$ is greater than the number of nonzero singular values of $A($meaning $s>$rank$(A)),$

raise a ValueError.

Use $np.$linalg.matrix$\_$rank$()$ to verify the rank of your approximation.