Question 1050772: How do I show proof for this problem?
If u∈V, then 1u=u
I have the following:
Let u= (a1, a2) where a1 and a2 are real numbers.
1(X)= [a1, a2] by substituting the coordinates in vector form.
1[a1,a2] = [1a1,1a2] by definition of scalar multiplication'
[1a1, 1a2] = [a1, a2] by definition of multiplicative identity of real numbers.
[a1, a2] = X by substitution.
Can anyone tell me if I did this correctly or if not please help me out.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! V is a vector space
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The unitary law of vector space states that, given u an element of V, then 1u is an element of V
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From the unitary law we know that 1u belongs to V
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let u = < u1, u2 > where u1 and u2 belong to R, then
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1 * u = <1u1, 1u2>, from scaler multiplication of a vector
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From the multiplicative identity property of real numbers, we know that
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1 * u1 = u1 and
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1 * u2 = u2
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therefore
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1 * u = u
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