Mathematics, 10.07.2019 03:30 JANA279
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?
Answers: 1
. So, each matrix is identified by its top-right coefficient, since the other three entries remain constant.![\phi:\ \mathbb{R} \to G,\quad \phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]](/tpl/images/0071/8322/2b08c.png)
. Then, you trivially have 
, 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]](/tpl/images/0071/8322/9da28.png)
![\phi(x) = \left[\begin{array}{cc}1&x\\0&1\end{array}\right]](/tpl/images/0071/8322/d7c87.png)
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)](/tpl/images/0071/8322/d46f6.png)
Another question on Mathematics
Mathematics, 21.06.2019 15:00
Which property is illustrated by the following statement? if hxa rgi, then rgi hxa.
Answers: 1
Mathematics, 21.06.2019 20:00
Two line segments are shown in the figure below. suppose that the length of the line along the x-axis is 6, and the length of the hypotenuse of the triangle is 10. what is the equation of the hypotenuse line (shown in red, below)?
Answers: 3
Mathematics, 21.06.2019 20:30
Which expression is equivalent to (4 +6i)^2? ? -20 + 48i 8 + 12i 16 - 36i 20 + 48i
Answers: 1
Mathematics, 21.06.2019 22:00
Type the correct answer in the box. consider the system of linear equations below. rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.
Answers: 2
You know the right answer?
Let g' be the group of real matricies of the form [1 x 0 1]. is the map that sends x to this matrix...
Questions
Chemistry, 19.10.2019 18:10
Arts, 19.10.2019 18:10
History, 19.10.2019 18:10
English, 19.10.2019 18:10
Mathematics, 19.10.2019 18:10
Mathematics, 19.10.2019 18:10
World Languages, 19.10.2019 18:10
English, 19.10.2019 18:10
Mathematics, 19.10.2019 18:10
Mathematics, 19.10.2019 18:10
