assign1_soln

# Assign1_soln - Math 136 Assignment 1 Solutions 2 0 4 1 1 is in the span of 1 1 0 1 Determine whether 6 3 2 2 Solution We need to determine whether

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Math 136 Assignment 1 Solutions 1. Determine whether 4 - 1 2 is in the span of 1 1 - 6 , 2 - 1 3 , 0 0 2 . Solution: We need to determine whether there exists coeﬃcients c 1 , c 2 , and c 2 such that 4 - 1 2 = c 1 1 1 - 6 + c 2 2 - 1 3 + c 3 0 0 2 Using operations on vectors on the right hand side, we get 4 - 1 2 = c 1 c 1 - 6 c 1 + 2 c 2 - c 2 3 c 2 + 0 0 2 c 3 = c 1 + 2 c 2 c 1 - c 2 - 6 c 1 + 3 c 2 + 2 c 3 Two vectors are equal if and only if there corresponding entries are equal. Thus, we have a system of 3 equations in 3 unknowns: c 1 + 2 c 2 = 4 c 1 - c 2 = - 1 - 6 c 1 + 3 c 2 + 2 c 3 = 2 We can solve this using substitution and elimination. Subtracting the second equation from the ﬁrst gives - 3 c 2 = - 5, so c 2 = 5 / 3. Substituting this into the ﬁrst equation we get c 1 + 2(5

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## This note was uploaded on 07/16/2011 for the course MATH 136 taught by Professor All during the Fall '08 term at Waterloo.

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Assign1_soln - Math 136 Assignment 1 Solutions 2 0 4 1 1 is in the span of 1 1 0 1 Determine whether 6 3 2 2 Solution We need to determine whether

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