chapter3.page10

# chapter3.page10 - functions, Example 2.1 . (1) v ( t ) =...

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10 1. BRIEF INTRODUCTION TO VECTORS AND MATRICES each column represents a eigenvector. Since multiplying an eigenvector by a nonzero constant you still get an eigenvector, so we can simplify the eigenvectors as v 1 = 1 + 3 2 , and v 2 = 1 - 3 2 Here is how to use Mathcad , Deﬁne the matrix by type A:[Ctrl][M] and specify the row and column number, ﬁll the entries. type eigenvals( , you will get eigenvals ( ) and in the place holder type A . Click at end of the eigenvals ( A ) and press [Shift][Ctrl][.], you will get eigenvals ( A ) . In the place holder type in key word simple . And click any area outside the box to get result. Using the same procedure for ﬁnd eigenvector using eigenvecs() function. 2. Vector-valued functions A vector-valued function over [a, b] is a function whose value is a vector or matrix. For example the following functions are vector-valued
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Unformatted text preview: functions, Example 2.1 . (1) v ( t ) = • t t 2 ‚ (2) x = 1 t 2 e t (3) A ( t ) = • 1 t 3-4 t + 5 sin( t ) ‚ 2.1. Arithmetics of vector-valued function. • To add two vector-valued function is to add their correspond-ing components. • To multiply a vector-valued function by a scalar function to to multiply each entry by the scalar function. • To multiply a vector(matrix) valued function to another vector-valued function is same as multiply a matrix with a vector. The following example illustrate how to add/subtract two vector-valued functions and how to multiply a vector-valued function by a scalar function and how to apply a vector-valued function that is matrix to a vector value function....
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## This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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