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snow_tiger [21]
3 years ago
13

What’s the answer? I’m very confused

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
6 0
F(x) = 29x +38. F(x) is a fancy way of saying y= and you must know the basic formula y=mx+b
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Let g' be the group of real matricies of the form [1 x 0 1]. Is the map that sends x to this matrix an isomorphism?
aliina [53]

Yes. Conceptually, all the matrices in the group have the same structure, except for the variable component x. So, each matrix is identified by its top-right coefficient, since the other three entries remain constant.

However, let's prove in a more formal way that

\phi:\ \mathbb{R} \to G,\quad \phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]

is an isomorphism.

First of all, it is injective: suppose x \neq y. Then, you trivially have \phi(x) \neq \phi(y), because they are two different matrices:

\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right],\quad \phi(y) = \left[\begin{array}{cc}1&y\\0&1\end{array}\right]

Secondly, it is trivially surjective: the matrix

\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]

is clearly the image of the real number x.

Finally, \phi and its inverse are both homomorphisms: if we consider the usual product between matrices to be the operation for the group G and the real numbers to be an additive group, we have

\phi (x+y) = \left[\begin{array}{cc}1&x+y\\0&1\end{array}\right] = \left[\begin{array}{cc}1&x\\0&1\end{array}\right] \cdot \left[\begin{array}{cc}1&y\\0&1\end{array}\right] = \phi(x) \cdot \phi(y)

8 0
3 years ago
Write this in standard form y+2=-3/4(x+1) that -3/4 is a fraction plz show work!!
pentagon [3]
Y+2=-3/4(x+1)
y+2=-3x/4 -3/4
y=-3x/4 - 3/4 - 2
y = -3x/4 - 3/4 - 8/4
y = -3x/4 - 11/4
7 0
3 years ago
How do I get the answer 4x4x4x4x4x4x4x4x4x4x4 thankssssss
jarptica [38.1K]
You calculate it which = 1,048,576
4 0
3 years ago
Read 2 more answers
Please help me! Due Thursday!
ikadub [295]

All the points are describing a rational number! (C)

6 0
3 years ago
If the perimeter of the following triangle is 7x-2, what is the length of the unknown side?
Alinara [238K]

7x-2-(3x-9)-(x+7)

=7x-2-3x+9-x-7

=7x-3x-x-2+9-7

=3x

4 0
3 years ago
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