1. Algebra II Honors Problem of the Day Homework page 721 11-35 eoo The following system has been solved and there are infinite solutions in the form of ( -3z, 2z+2, z ). Name one specific solution of the system. x - y + 5z = -2 2x + y + 4z = 2 2x + 4y - 2z = 8

2. A Matrix is a rectangular array of numbers with m rows and n columns. A matrix has dimensions m x n in size. We will use a matrix to represent systems of linear equations. This type of matrix is called an augmented matrix. x - y + 5z = -2 2x + y + 4z = 2 2x + 4y - 2z = 8 [ 1 -1 5 -2 ] [ ] [ 2 1 4 2 ] [ ] [ 2 4 -2 8 ]

3. Reduced Row-Echelon Form Row-Echelon Form [ 1 0 0 2 ] [ ] [ 0 1 0 4 ] [ ] [ 0 0 1 -2 ] [ 1 -3 4 2 ] [ ] [ 0 1 -2 4 ] [ ] [ 0 0 1 -2 ]

4. Row Operations for Augmented Matrices 1.Rows may be switched. 2.A row may be multiplied by any non-zero number. 3.Two rows may be added or subtracted. The resulting sum or difference may replace either of the rows involved in the sum or difference. When trying to produce row-echelon form: 1.Get ones in appropriate positions by using mult/div. 2.Get zeros below the ones by using mult./div. in combination with add./sub.