Determine whether a couple of given systems of equations

Question

1. Determine whether a couple of given systems of equations are equivalent or not?

(a)

x - 4y + 5z = 27

y - 7z = -54

z = 8

(b)

x - 6y + z = 15

y + 5z = 42

z = 8

2. Determine whether a couple of given systems of equations are equivalent or not?

(a)

x + 3y -z = 19

y + 6z = -18

z = -4

(b)

x - y + 3z = -15

y -2z = 14

z = -4

3. Find the matrix in reduced row echelon form

x + 3y + z = 3

x + 5y + 5z = 1

2x + 6y + 3z = 8

4. Find the matrix in reduced row echelon form

I₁ - I₂ + I₃ = 0

3I₁ + 4I₂ = 18

I₂ + 3I₃ = 6