MATH 6A- Midterm Exam Guide - Comprehensive Notes for the exam ( 18 pages long!)
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These functions take in a real number and output a real number. Vectors can be parallel even if they point in opposite directions. Use dot product to test for orthogonality (in any dimension) and cross product to test. Theorem 1. 10: the cross product is orthogonal to both and . Scalar triple product = for any three vectors in . Consider the detrminant of a matrix with two identical rows. Theorem 1. 11: nonzero vectors and in are parallel if and only if whether vectors are parallel in. A function is a rule that assigns an element of to each element in. Given a function , is called the domain of and is called the range/codomain. Example: the vector-valued function has two components (since output is in ) The functions above are all examples of real-valued functions, or scalar functions. We"ll often talk about the component function of a vector-valued function. These functions take in a vector and output a real number.
