]Eigenvectors are found by the equation
![(A-\lambda I) \vec{v} = 0$](https://tex.z-dn.net/?f=%28A-%5Clambda%20I%29%20%5Cvec%7Bv%7D%20%3D%200%24)
implying that
![\det(A-\lambda I) = 0](https://tex.z-dn.net/?f=%5Cdet%28A-%5Clambda%20I%29%20%3D%200)
. We then can write:
And:
Gives us the characteristic polynomial:
![\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6](https://tex.z-dn.net/?f=%20%5Clambda%5E2%20-%205%20%5Clambda%20-6%20%3D%200%20%5Cimplies%20%5Clambda_1%20%3D%20-1%2C%20%5Clambda_2%20%3D%206)
So, solving for each eigenvector subspace:
![\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]](https://tex.z-dn.net/?f=%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204%20%26%202%20%5C%5C%205%20%26%201%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20x%20%5C%5C%20y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20-x%20%5C%5C%20-y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20)
Gives us the system of equations:
Producing the subspace along the line
![y = -\frac{5}{2} x](https://tex.z-dn.net/?f=%20y%20%3D%20-%5Cfrac%7B5%7D%7B2%7D%20x%20)
We can see then that 3 is the answer.
Answer:
X=2
Step-by-step explanation:
Cross multiply you'll get:
4(2x-1)=3(5x-6)
8x-4=15x-18
8x-15x=4-18
-7x=-14
x=2
Answer:
n=-1
Step-by-step explanation:
distribute the 7 to n+4 to get 7n + 28 = 21. subtract 28 from both sides to get 7n = -7. divide both sides by 7 to get n=-1
you could also divide everything by 7 at the beginning to get n+4=3, then subtract 4 from both sides to get n=-1
Answer:
3/5
Step-by-step explanation:
You divide 1 and 3. Keep the denominator since it is the same number
Hope this was helpful, Have a Great Day!!
Answer:
a. 42
Step-by-step explanation:
What I did was I multiplied each one by 35. (The formula for finidng area is width times length and we already know the area, 1470.) 1435x35 is way too big, 44x35 is 1540 still too big, but 42x35 is 1470 and the area is 1470 ft squared therefor, 42 is your answer.