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patriot [66]
3 years ago
14

Can you please answer this ASAP!! (20 points!!)

Mathematics
1 answer:
Elanso [62]3 years ago
7 0

Answer the question 1st:

1-corresponding angles=180

then,90+90=180

2-not parallel

3-not parallel

4-corresponding angles=180

          x+x=180

          2x=180

          x=180/2

          x=90degree

5-suppose x for two angles

then, same as 4 no. x + x=180

6= alternate angles are always equal.

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16. Let W be the set of all vectors in R3 of the form a+2b b -3a Find a basis for Wand state the dimension of W.
Yuki888 [10]

Answer:

W=\{\left[\begin{array}{ccc}a+2b\\b\\-3a\end{array}\right]: a,b\in\mathbb{R} \}

Observe that if the vector x=\left[\begin{array}{ccc}x\\y\\z\end{array}\right] is in W then it satisfies:

\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{c}a+2b\\b\\-3a\end{array}\right]=a\left[\begin{array}{c}1\\0\\-3\end{array}\right]+b\left[\begin{array}{c}2\\1\\0\end{array}\right]

This means that each vector in W can be expressed as a linear combination of the vectors \left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]

Also we can see that those vectors are linear independent. Then the set

\{\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]\} is a basis for W and the dimension of W is 2.

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