**Unformatted text preview: **1.5.2 Cartesian form of a plane in R3 You learnt from high school that an equation of a straight line can be written in the form ar+by+c =
0. Such an equation is called a linear equation in two variables. The set of all points (as, 3;) which
satisfy the equation is a straight line. Now we deﬁne linear equations in n variables and interpret
them geometrically in the special case n = 3. Deﬁnition 5.. A linear equation in as variables (or unknowns) $1,312, . . . ,3”, is
an equation of the form (11331 + {12132 + - -- + ans?” 2 b, where all . . . ,an and b are scalars. 331
Only in R3, a plane can be described by a single linear equation. For x = 332 , consider the
373
linear equation in the three variables 2:1, 2:2, 3:3 given by {1331 + b.3132 +cas'3 = d, where a. b. c. d are ﬁxed scalars. Now if o: i O. we can solve the eouation to ﬁnd {171 in terms of ma ...

View
Full Document

- Fall '08
- Staff
- Linear Algebra, Algebra