MATH125 Lecture Notes - Lecture 3: Commutative Property, Distributive Property, Scalar Multiplication

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

Everything we did extends easily to three dimensions. The set of all ordered triples of real numbers is denoted by r3. Points and vectors are located using three mutually perpendicular coordinate axes that meet at the origin o. A point such as a = (1, 2, 3) can be located as follows. First travel 1 unit along the x-axis, then move 2 units parallel to the y-axis, and nally move 3 units up parallel to the z-axis. The corresponding vector u = [1, 2, 3] is then. In general, we de ne rn as the set of all ordered n-tuples of real numbers written as row or column vectors. The individual entries of v are its components (or coor- dinates); vi is called the i-th component (or i-th coordinate). We extend the de nitions of vector addition and scalar multiplication in the obvious way: if u = [u1, .