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RSB [31]
3 years ago
7

Order the following from smallest to largest. .84, 2.83, .065

Mathematics
1 answer:
Paladinen [302]3 years ago
4 0

Answer:

.065, .84, 2.83

Step-by-step explanation:

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<em>First. </em>Let us prove that \ker L is not empty. This is easy because L(0_V)=0_W, by linearity. Here, 0_V stands for the zero vector of V, and 0_W stands for the zero vector of W.

<em>Second.</em> Let us prove that \alpha x\in\ker L. By linearity

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<em>Third. </em> Let us prove that y+ x\in\ker L. Again, by linearity

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And the statement readily follows.

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\alpha u = \alpha L(x) = L(\alpha x) = L(z).

Then, there exist an element z\in V such that L(z)=\alpha u. Thus \alpha u is in the range of L.

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u+v = L(x)+L(y) = L(x+y)=L(z).

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Notice that in this second part of the problem we used the linearity in the reverse order, compared with the first part of the exercise.

Step-by-step explanation:

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