Consider a linear system Ax=b. Assume that column vectors a1,....,an ∈ Rn are columns of matrix A ie.

A = [a1 a2 a3 .... an]. Let C = [A|b] be the augmented matrix associated with this linear system.

Let us consider 2 different scenarios

a) Suppose I interchange column ai and ak of the augmented matrix C giving a new matrix C1 (i,k

<= n). Now I solve the problem assuming C1 is my augmented matrix. How are the solutions

of augmented matrix C and C1 related.

b) Suppose I scale the i

th column of the augmented matrix C by α giving a new matrix C2 (i,k <=

n). Now I solve the problem assuming C2 is my augmented matrix. How are the solutions of

augmented matrix C and C2 related.