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# Week2 - equation A~x = ~ where ~x = x 1 x 2 x 3 By...

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Solutions for Assignment 2 Applied Linear Algebra MATH 232 (Fall 2008) Section 1.4 Section 1.5

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Assignment 2 Applied Linear Algebra Math 232(Fall 2008) Additional question: Suppose that you have a homogenous system of linear equations in 3 variables x 1 , x 2 , x 3 . Show that if x 1 = c 1 , x 2 = c 2 , x 3 = c 3 and x 1 = d 1 , x 2 = d 2 , x 3 = d 3 are two solutions then x 1 = c 1 + d 1 , x 2 = c 2 + d 2 , x 3 = c 3 + d 3 is also a solution. (Hint: a homogeneous system corresponds to a matrix equation with the zero vector on the right.) A1. A homogeneous system of linear equations in three variables corresponds to a matrix
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Unformatted text preview: equation A~x = ~ , where ~x = x 1 x 2 x 3 . By assumption, the vectors c 1 c 2 c 3 and d 1 d 2 d 3 are solutions to this equation. This means A c 1 c 2 c 3 = ~ and A d 1 d 2 d 3 = ~ . But now A c 1 + d 1 c 2 + d 2 c 3 + d 3 = A c 1 c 2 c 3 + A d 1 d 2 d 3 = ~ 0 + ~ 0 = ~ . 1...
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Week2 - equation A~x = ~ where ~x = x 1 x 2 x 3 By...

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