2331_Notes_1o1_fill - Math 2331 Linear Algebra Section 1.1...

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Math 2331 Linear Algebra Section 1.1 Vectors A VECTOR is an ordered n-tuple of real numbers arrayed in one row or one column. Examples: ) as a row vector, or as a column vector. 2 3 5 9 ⎛⎞ ⎜⎟ ⎝⎠ ( 2,3,5,9 Define a vector by a lower case letter in bold type (sometimes) and each entry in the vector by the same letter with a subscript to indicate which entry it is. For example, v= w= 1 2 3 v v v 1 2 3 4 w w w w If w= , then 2 3 5 9 1234 2, 3, 5, 9 wwww = === Two vectors are equal if they are the same size (i.e. have the same number of entries) and the corresponding entries are the same real number. 1 2 3 4 w w w w = if and only if 3 7 2 5 A SCALAR is a real number. Recall that the set of real numbers is a field with respect to addition and multiplication. This idea of a vector being an ordered list of real numbers and a scalar being a single real number generalizes to the entries in a vector being any elements out of a field and the scalars being single elements of the field. But, we will only touch on this issue in this
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This note was uploaded on 08/10/2011 for the course MATH 2331 taught by Professor Staff during the Spring '08 term at University of Houston.

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2331_Notes_1o1_fill - Math 2331 Linear Algebra Section 1.1...

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