Yes. Conceptually, all the matrices in the group have the same structure, except for the variable component . 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
is an isomorphism.
First of all, it is injective: suppose . Then, you trivially have , because they are two different matrices:
Secondly, it is trivially surjective: the matrix
is clearly the image of the real number x.
Finally, 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
ΔQTR and ΔSTP are similar triangles. The corresponding sides of similar triangles are the same length.
TR = PT
TS = QT
Input the algebraic expression to make an equation system
PT = TR
y = 2x - 1 <em>(first equation)</em>
TS = QT
6x + 13 = 5y
6x - 5y = -13 <span><em>(second equation)</em>
</span>Using subtitution method, subtitute y with 2x - 1 from first equation into the second equation, to find the value of x
6x - 5y = -13
6x - 5(2x - 1) = 13
6x - 10x + 5 = 13
-4x + 5 = 13
-4x = 13 - 5
-4x = 8
x = 8/-4
x = -2
Find y with subtituting x with -2 in the first equation
y = 2x - 1
y = 2(-2) - 1
y = -4 - 1
y = -5
Answer:
x = -2
y = -5
So you're initial equation is
. Well since
, plug in 24 for the 1 in
. So
, and
so
.
Answer:
Step-by-step explanation:
Let the invested amount is x.
<u>Then the interest amount is:</u>
- x*5*2.25/100 = 675
- 0.1125x = 675
- x = 675 / 0.1125
- x = 6000
Correct choice is A
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