Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D)
≠ 0
Determinant of a 3x3 matrix is calculated by:
det ![\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]\left[\begin{array}{ccc}1&\beta\\2&2\\2-2\beta&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%261-%5Cbeta%5C%5C2%262%260%5C%5C2-2%5Cbeta%264%260%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cbeta%5C%5C2%262%5C%5C2-2%5Cbeta%264%5Cend%7Barray%7D%5Cright%5D)
![8(1-\beta)-[2(2-2\beta)(1-\beta)]](https://tex.z-dn.net/?f=8%281-%5Cbeta%29-%5B2%282-2%5Cbeta%29%281-%5Cbeta%29%5D)
β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.
Answer:
Graph C is the answer.
Step-by-step explanation:
From the graphs attached,
Graph A
Given graph represents a cubic function.
Graph B
This graph represents a piecewise function.
Graph C
This graph represents an exponential function.
Graph D
Given graph represents a quadratic function.
Graph C is the answer.
Answer:
The all-time medal table for all Olympic Games from 1896 to 2018, including Summer Olympic Games, Winter Olympic Games, and a combined total of both, is tabulated below. These Olympic medal counts do not include the 1906 Intercalated Games which are no longer recognized by the International Olympic Committee (IOC) as official Games. The IOC itself does not publish all-time tables, and publishes unofficial tables only per single Games. This table was thus compiled by adding up single entries from the IOC database.[1]
The results are attributed to the IOC country code as currently displayed by the IOC database. Usually, a single code corresponds to a single National Olympic Committee (NOC). When different codes are displayed for different years, medal counts are combined in the case of a simple change of IOC code (such as from HOL to NED for the Netherlands) or simple change of country name (such as from Ceylon to Sri Lanka). As the medals are attributed to each NOC, not all totals include medals won by athletes from that country for another NOC, such as before independence of that country. Names in italic are national entities that no longer exist. The totals of NOCs are not combined with those of their predecessors and successors.
Step-by-step explanation:
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