MAT133Y1 Lecture Notes - Lecture 6: Row Echelon Form, 7Z, Invertible Matrix
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Mat133y1y - lecture 6 - 6. 4: a system of linear equations (continued), 6. 5-6. 6: row. Change a row by adding to it, a constant multiple of some other row. The last matrix is in row echelon form: Any row of zeros (to the left of the partition) is at the bottom. The first non-zero entry in each of the other rows is a 1. Every leading element is to the right of the leading element of the preceding rows. These imply: the entries below any leading element are all zero. The last matrix is also in reduced row echelon form, which means it satisfies the above properties and also: if a column has a leading element, all other elements are 0. 5 which represents the system: x=4, y=2, z=5. A given system is of one of three types: Some systems have more than two solutions. 3w - x + 4y + 5z = -2.
