MATH 330 H42

MATH 330 H42 - Math 330 Homework 4.2 (Pages 234,235) (6)...

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Unformatted text preview: Math 330 Homework 4.2 (Pages 234,235) (6) Find an explicit description of Nul A , by listing vectors that span the null space. A = 1 5- 4- 3 1 0 1- 2 1 0 0 SOLUTION: We perform row operations in order to solve Avectorx = vector 0. Note that since the matrix is already in Echelon form, we continue to get reduced Echelon form. R 1 ← R 1- 5 R 2 = ⇒ 1 0 6- 8 1 0 1- 2 1 0 0 = ⇒ x 1 =- 6 x 3 + 8 x 4- x 5 x 2 = 2 x 3- x 4 = ⇒ x 1 x 2 x 3 x 4 x 5 = x 3 - 6 2 1 5 + x 4 8- 1 1 + x 5 - 1 1 So a basis for the Null space of A is - 6 2 1 5 , 8- 1 1 , - 1 1 (10) Show the given set is a vector space or find an example to the contrary:...
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.

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MATH 330 H42 - Math 330 Homework 4.2 (Pages 234,235) (6)...

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