# Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 711: 79

x = 0 y = -4a + 2 z = a Where a is any real number

#### Work Step by Step

The reduced row-echelon form of the matrix is: $\begin{bmatrix} 1 & 0 & 0 & |0\\ 0 & 1 & 4 & |2\\ 0 & 0 & 0 & |0\\ 0 & 0 & 0 & |0\\ \end{bmatrix}$ We can write the solution as: x = 0 y + 4z = 2 We then can write the system in terms of z: x = 0 y = -4z + 2 To not use one of the basis variables we can use a: x = 0 y = -4a + 2 z = a Where a is any real number

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