{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hmwk6

# hmwk6 - product(b Deﬁne a vector ~ b that is given by the...

This preview shows page 1. Sign up to view the full content.

Department of Chemical Engineering University of California, Santa Barbara Eng 5A Fall 2001 Instructor: David Pine Homework #6 Homework due: Wednesday, 6 November 2001 1. Consider the following matrix: M = a b c 0 d e 0 0 f (a) Form the partitioned matrix [ M | I ] and row-reduce this to ﬁnd the inverse M - 1 of M . Then verify that you have found the inverse by doing the multiplication M - 1 M . For this part use Mathematica only to multiply and/or add rows together. (b) Find the inverse M - 1 by deﬁning the matrix A = [ M | I ] and then row reducing A using the RowReduce function of Mathematica . (c) Find the inverse M - 1 using the Inverse function of Mathematica . Verify that you obtain the same result for M - 1 using all three methods (d) Fine the determinant of M and M - 1 and verify that their product is unity. 2. The three points (1 , 1 , 2), (2 , 0 , 0), (0 , - 1 , 1) deﬁne a plane. Use vectors to ﬁnd an ( x, y, z ) equation for the plane that contains these three points. Employ the following method using Mathematica . (a) Find a vector ~n perpendicular to the plane containing three points using the cross
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: product. (b) Deﬁne a vector ~ b that is given by the diﬀerence between an arbitrary point ( x, y, z ) and one of the three points that deﬁne the plane. Note that ( x, y, z ) will be in the plane deﬁned by our three points if the vector ~ b is perpendicular to ~n . Use the Solve command of Mathematica to ﬁnd the condition (equation for x , y , and z ) that satisﬁes the equation ~ b · ~n = 0. Verify that the three points satisfy the equation you ﬁnd. (c) Use your solution to ﬁnd a parametric expression for the plane in R 3 that contains the three points (1 , 1 , 2), (2 , , 0), (0 ,-1 , 1). That is, ﬁnd the column matrix (vector) ~x such that ~x = ~ P + t 1 ~ b 1 + t 2 ~ b 2 , where ~x = ( x, y, z ), ~ P is a particular column matrix, and t 1 and t 2 are numbers (scalars), and where ( x, y, z ) are points in the plane deﬁned by the three points (1 , 1 , 2), (2 , , 0), (0 ,-1 , 1)....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online