Choose letters to represent the unknowns: x and y. We are told that x-y = 361.
We could choose any number for x and then calculate y:
Suppose we let x = 500. Then 500 - y = 361, and y = 139.
Suppose we let x = 1. Then 1 - y = 361, and y = -360.
And so on.
To write 2^7, you would do 2*2*2*2*2*2*2 because your multiplying 2 by itself 7 times. The only factor is, 2. Now try and do the rest, if you still need help, comment and I'll edit my answer and give you more hints. you got this. I believe in you :)
Answer:
A = 1,144 ft²
Step-by-step explanation:
The base of the quadrilateral is also x. We know this since there are 2 90° angles, there fore the other 2 angles are also 90°, making the top and bottom sides of the quadrilateral parallel to each other, and equal in measure.
Since the entire base of the yard is 2x, the base of the triangle is x.
The area of the triangle is
A = (1/2)bh where b is the base, and h is the height
For this example...
A = (1/2)x(44) (x is the base, and 44 is the height)
So
A = (1/2)(44)x
A = 22x
The area of the quadrilateral is
A = LW
A = 44x
The total area of the yard is
A = 22x + 44x
A = 66x
We are told that the entire area is 3,462. so
3,462 = 66x now solve for 'x'
3,462/66 = x (divide both sides by 66)
52 = x
So the area of the picnic tables is the area of the triangle, which is
A = 22(52) = 1,144 ft²
With
we have
so 
has one eigenvalue, 
, with multiplicity 3.
In order for to not be defective, we need the dimension of the eigenspace to match the multiplicity of the repeated eigenvalue 2. But 
has nullspace of dimension 2, since
That is, we can only obtain 2 eigenvectors,
and there is no other. We needed 3 in order to complete the basis of eigenvectors.
