MATH125 Lecture Notes - Lecture 9: Scalar Multiplication, Dot Product, Diagonal Matrix

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: George Peschke

Document Summary

V + 2w - 2y - z = -1 v - 3w + x + y + z = 3. Add x1 row 1 to row 2, subtract x2 row 1 form row 3, subtract x3 row 1 form row 4. Subtract row 3 from rows 1 and 4. The rank of a matrix is defined as the number of leading ones in the rref. To find the solutions of a system of linear equations, we transform it into. Solutons of a system in rref can be computed as follows: Solve for the variable associated to each leading 1. A system has no soluton exactly when its rref has a leading 1 in the augmentation column; such a system is called, "inconsistent" A system has exatly one solution if and only if each variable is bound to a leading 1, and there is no leading 1 in the augmentation column.