Linear Algebra with Applications (3rd Edition)

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110.201 Linear Algebra 2nd Quiz February 10, 2005 Problem 1 Consider the vector ~v = 1 2 3 in R 3 1. Determine the equation of the plane V through the origin and orthogonal to ~v . 2. Consider the vector ~w = 4 5 6 in R 3 and find ref V ( ~w ). Problem 2 Is the following matrix invertible? A = 1 0 1 2 - 1 0 0 1 1 Justify your answer. If A - 1 exists, find it.
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Unformatted text preview: Problem 3 * Dene the linear transformation T A : R 3 R 3 (i.e. write the matrix A ) whose kernel Ker( T A ) is the line through the origin and parallel to the vector 1 1 and whose image Image( T A ) is the plane x + z = 0. Justify your answer. 1...
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