NYC.L4

# NYC.L4 - MAT-NYC LAB#4 Subspaces Linear Spans Solution...

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MAT-NYC LAB #4 Subspaces - Linear Spans - Solution Spaces 1. Rewrite the following as a vector equation. a) The linear system - 2 x 1 + 6 x 2 + x 3 - 7 x 4 = - 1 x 1 + 5 x 2 - 1 2 x 4 = 0 2 x 2 - 3 x 3 = 5 . b) The matrix equation ± 4 - 2 - 5 9 - 7 1 - 8 - 3 ² 2 6 - 1 0 = ± 1 0 ² 2. Rewrite the vector equation 6 ± 3 1 ² + 2 ± - 5 2 ² - ± 0 - 1 ² = ± - 4 7 ² as a matrix equa- tion. 3. Which of the following subsets of R 3 are subspaces? Justify your answers. a) { [ a,a 2 ,b ] } ; b) { [ x,y,z ] such that xyz = 1 } ; c) { [ x,y,z ] such that xy = 0 } . 4. Show that 2 0 0 belongs to the column space of A = 1 - 1 1 1 1 - 1 - 1 1 1 . 5. If possible, write the vector ~u = [11 , - 5 , 9] as a linear combination of the vectors ~v 1 = [1 , 0 , 1], ~v 2 = [ - 2 , 1 , - 2] and ~v 3 = [ - 6 , 3 , - 5]. Do the three vectors ~v 1 , ~v 2 and ~v 3 span R 3 ? 6. Let ~u 1 = [1 , 3 , - 1] and ~u 2 = [ - 5 , - 8 , 2]. a) For what values of

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## This note was uploaded on 09/26/2011 for the course BIO 293 taught by Professor John during the Spring '11 term at Harvard.

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NYC.L4 - MAT-NYC LAB#4 Subspaces Linear Spans Solution...

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