Implementation in python

Approximating a Condition Number 10 points You wish to approximate the condition number of an n n matrix A in the two-norm. However, you are not given A itself. Instead, you are given a matrix B = ( where the columns of X are randomly chosen vectors with unit two-norms. Estimate of the norm of A by considering the relative increase in norm observed in columns of B, and store it in norm A.Consider the least increase in norm for any column of B and use it to estimate the 2-norm condition number of A, storing it as cond_A Now, given a second matrix Y such that X - AY, use its columns to better estimate |IA-112 and store this estimate in norm A inv. Then use this estimate combined with norm A to estimate the condition number of A and store it as cond_A2 Using print),explain why cond A2 is so much better compared to cond A NPUT B:2-d numpy array of shape (50, 1000), represents the matrix product AX . Y:2-d numpy array of shape (50, 1000) , represents the matrix product AX OUTPUT norm_A: approximation of |Al l2 using B cond A: approximation of (A) using only B . norm_A_inv: approximation of ||Al2 using Y cond_A2: approximation of k (A) using both Band Y Approximating a Condition Number 10 points You wish to approximate the condition number of an n n matrix A in the two-norm. However, you are not given A itself. Instead, you are given a matrix B = ( where the columns of X are randomly chosen vectors with unit two-norms. Estimate of the norm of A by considering the relative increase in norm observed in columns of B, and store it in norm A.Consider the least increase in norm for any column of B and use it to estimate the 2-norm condition number of A, storing it as cond_A Now, given a second matrix Y such that X - AY, use its columns to better estimate |IA-112 and store this estimate in norm A inv. Then use this estimate combined with norm A to estimate the condition number of A and store it as cond_A2 Using print),explain why cond A2 is so much better compared to cond A NPUT B:2-d numpy array of shape (50, 1000), represents the matrix product AX . Y:2-d numpy array of shape (50, 1000) , represents the matrix product AX OUTPUT norm_A: approximation of |Al l2 using B cond A: approximation of (A) using only B . norm_A_inv: approximation of ||Al2 using Y cond_A2: approximation of k (A) using both Band Y