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
≠ 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:Q=1.39 or -0.103
Step-by-step explanation:
I think it's need to be a graph right?
<h3>Answer 1a :- </h3>
Here we can solve this question using<em> </em><em>Unitary</em><em> </em><em>Method</em><em> </em><em>.</em> As ;
→ In 17hrs the boat travels 452km
→ In 1hr the boat will travel 452km/17
→ In 9hrs the boat will travel 452/17km * 9 = 239.29km

<h3>Answer 1b:-</h3>
→ A car can travel 156km on 13L gasoline .
→ It will travel 1km on 13/156L of gasoline .
→ It will travel 480km on 13/156*480L = 40L of gasoline .

<h3>
Answer 2a :-</h3>
→ A boat can go 180 miles on 60L gasoline.
→ It will go 1mile in 60/180L of gasoline.
→ It will go 306 miles in 60/180*306L = 102L of gasoline .

<h3>Answer 2b :-</h3>
→ On 51L of gasoline a car can go 408km
→ On 1L of gasoline car will go 408/51 km
→ On 11L of gasoline it will go 408/51*11L = 88km
