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:
We know our answer is correct because 11 + 12 + 13 equals 36 as displayed Below
Explanation
3X + 3 = 36 3X + 3 - 3 = 36 - 3 3X = 33 3X/3 = 33/3 X = 11 Which means that the first number is 11, the second number is 11 + 1 and the third number is 11 + 2. Therefore, three consecutive integers that add up to 36 are 11, 12, and 13. 11 + 12 + 13 = 36 We know our answer is correct because 11 + 12 + 13 equals 36 as displayed above. Therefore, three consecutive integers that add up to 36 are 11, 12, and 13. 11 + 12 + 13 = 36
Plz mark brainliest if helps Also hope helps:)
Answer:
2 (4x - 1) + 6 = 8x + 4 = 4(2x+1)
Step-by-step explanation:
2 (4x - 1) + 6
= (2*4x + 2*-1) + 6
= 8x - 2 + 6
= 8x + 4
= 4/(2x+1)
So product means multiplication so -2*(x-6) > -18 so divide by -2 on both sides to get x-6<9 because when you multiply a negative the sign swaps directions and then add 6 to get x<15
