I'm really struggling to understand what I supposed to do thank you
Show that the elementary row operation of row replacement preserves the solution set of the system. For notational convenience, you may assume the system is 3 × 3. Thus, show that if (s1,s2,s3) is a solution of the original system, then it is also a solution of the transformed system, and vice versa. Hint: Let the original system be
a11x1 + a12x2 + a13x3 = b1
a21x1 + a22x2 + a23x3 = b2
a31x1 + a32x2 + a33x3 = b3
and assume that we multiply the second row by a scalar c and add it to the first row. That is, the transformed system is
a11x1 +a12x2 +a13x3 +c·(a21x1 +a22x2 +a23x3) = b1 +c·b2
a21x1 + a22x2 + a23x3 = b2
a31x1 + a32x2 + a33x3 = b3
First, assume that (s1, s2, s3) is a solution of the original system, and show that it is a solution of the transformed system. Then, assume that (s1,s2,s3) is a solution of the transformed system, and show that it is a solution of the original system.