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Unformatted text preview: plane related to each other? Problem 3. Let A be an n m matrix. Assume that there exists an m n matrix B such that B A = I n . Show that rank( A ) = m . Must A necessarily be invertible? Problem 4. Consider the linear transformation T : R 3 R 3 dened by T ( ~x ) = A~x in terms of the 3 3 matrix A = 1 7 2 3 6 36 2 6 23 . a. Show that T is an orthogonal transformation. b. Find the matrix of the inverse of T . Problem 5. Let V be a linear space with inner product hi . Prove the Law of Cosines : Show that if is the angle between f,g V , then  fg  2 =  f  2 +  g  22 cos  f  g  ....
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This note was uploaded on 03/31/2012 for the course MA 351 taught by Professor ?? during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 ??
 Linear Algebra, Algebra

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