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1.4 Linear Comb.

# 1.4 Linear Comb. - 1.4 1.4 Linear Combinations and Systems...

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1.4. 1.4. Linear Combinations and Systems of Linear Equations 1 . (a) T (0 v = 0 , v V ) (b) F (p.30 span ( ) = { 0 } ) (c) T (p.30 Theorem 1.5) (d) F (p.27) (e) T (p.27) (f) F (p.33 2(b)) 2 . (a) { r (1 , 1 , 0 , 0) + s ( - 3 , 0 , - 2 , 1) + (5 , 0 , 4 , 0) | r,s R } (b) ( - 2 , - 4 , - 3) (c) There are no solutions (d) { r ( - 8 , 3 , 1 , 0) + ( - 16 , 9 , 0 , 2) | r R } (e) { r (0 , - 3 , 1 , 0 , 0) + s ( - 3 , - 2 , 0 , 1 , 0) + ( - 4 , 3 , 0 , 0 , 5) | r,s R } (f) (3 , 4 , - 2) 3 . (a) yes ( - 2 , 0 , 3) = 4(1 , 3 , 0) + ( - 3)(2 , 4 , - 1) (b) Yes (1 , 2 , - 3) = 5( - 3 , 2 , 1) + 8(2 , - 1 , - 1) (c) No (d) Yes (2 , - 1 , 0) = 4 5 (1 , 2 , - 3) + 6 5 (1 , - 3 , 2) (e) No (f) Yes ( - 2 , 2 , 2) = 4(1 , 2 , - 1) + 2( - 3 , - 3 , 3) 19 PNU-MATH

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1.4. 4 . (a) Yes ( x 3 - 3 x + 5) = 3( x 3 + 2 x 2 - x + 1) + ( - 2)( x 3 + 3 x 2 - 1) (b) No (c) Yes 4 , - 3 (d) Yes - 2 , 5 (e) No (f) No 5 . (a) Yes (2 , - 1 , 1) = 1(1 , 0 , 2) + ( - 1)( - 1 , 1 , 1) span ( S ) (b) No (c) No (d) Yes 2 , - 1 (e) Yes - 1 , 3 , 1 (f) No
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1.4 Linear Comb. - 1.4 1.4 Linear Combinations and Systems...

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