Answer:
![\left[\begin{array}{ccc}3&-1&\\-1&1/2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-1%26%5C%5C-1%261%2F2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The matrix system for the linear equations: x + 2y = 8, 2x + 6y = 9
![\left[\begin{array}{ccc}1&2&\\2&6\\\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}8\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%26%5C%5C2%266%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
To get the coefficient of x and y, the inverse of the first matrix (let the first matrix be A) must be known.
= (1 / determinant of A) x Adjoint of A
the determinant of A = (1 x 6) - (2 x 2) = 6 - 4 = 2
Adjoint of A = ![\left[\begin{array}{ccc}6&-2&\\-2&1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%26%5C%5C-2%261%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\frac{1}{2} \left[\begin{array}{ccc}6&-2\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%26-2%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
=
Let's go through each answer choice and eliminate the choices.
a) 6(2/3) = 4, this is less than 6, making it our correct answer, but still go and check each answer
b) 6(2/3) again = 4, this is less than 6, making this answer choice wrong.
c) 6(3/2) = 9, this is greater than 6, making this answer choice wrong.
d) 6(3/3) = 6, this is equal to 6, making this answer choice wrong.
6a - (b - (3a - (2b + c + 4a - (a + 2b - c))))
6a - (b - (3a - (2b + c + 4a - a - 2b + c)))
6a - (b - (3a - (2b - 2b + 4a - a + c + c)))
6a - (b - (3a - (3a + 2c)))
6a - (b - (3a - 3a - 3c))
6a - (b - 3a + 3a + 3c)
6a - (b + 3c)
6a - b - 3c
x³ + x² - 25x - 25
x²(x) + x²(1) - 25(x) - 25(1)
x²(x + 1) - 25(x + 1)
(x² - 25)(x + 1)
(x² - 5x + 5x - 25)(x + 1)
(x(x) - x(5) + 5(x) - 5(5))(x + 1)
(x(x - 5) + 5(x - 5))(x + 1)
(x + 5)(x - 5)(x + 1)
36x² + 60x + 25
36x² + 30x + 30x + 25
6x(6x) + 6x(5) + 5(6x) + 5(5)
6x(6x + 5) + 5(6x + 5)
(6x + 5)(6x + 5)
(6x + 5)²
6×4=24+5=29 inches squared
For this case we have to by definition, if two lines are perpendicular then the product of its slopes is -1.
That is to say:
We have the following equation:
So:
Thus:
Thus, a line perpendicular to the given line must have slope 
Option A:
It is not perpendicular!
Option B:
If it is perpendicular!
Option C:
It is not perpendicular!
Option D:
It is not perpendicular!
The correct option is option B
ANswer:
Option B
