201Quiz2TR

# 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 = 6 2 3 in R 3 1. Determine the equation of the line L through the origin and parallel to ~v . 2. Consider the vector ~w = 3 4 5 in R 3 and find proj L ( ~w ). Problem 2 Is the following matrix invertible? A = 2 1 0 1 - 1 3 - 1 0 1 Justify your answer. If A - 1 exists, find it.
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Unformatted text preview: Problem 3 * Given the linear subspace V of R 3 deﬁned by the equation 2 x-y + z = 0 V = { ( x,y,z ) ∈ R 3 | 2 x-y + z = 0 } ﬁnd matrices A and B (and corresponding linear transformations T A and T B ) such that 1. Ker( T A ) = V 2. Image( T B ) = V . 1...
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