Answer:
This is simple. And, you best not be cheating either.
15 - 1 x 18 / 6
1x18 = 18
18/6 is 3.
15 - 3 = 12
12 is the answer.
Step-by-step explanation:
This question is incomplete, the complete question is;
Determine if the described set is a subspace. Assume a, b, and c are real numbers.
The subset of R³ consisting of vectors of the form ![\left[\begin{array}{ccc}a\\b\\c\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%5C%5Cb%5C%5Cc%5Cend%7Barray%7D%5Cright%5D)
, where abc = 0
- The set is a subspace
- The set is not a subspace
Answer:
Therefore; The set is not a subspace
Step-by-step explanation:
Given the data the question;
the subset R³;
S = { , where abc = 0 }
we know that a subset of R³ is a subspace if it stratifies the following properties;
- it contains additive identity
- it is closed under addition
- it is closed under scales multiplication
Looking at the properties, we can say that it is not a subspace
As;
u = ![\left[\begin{array}{ccc}1\\1\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C1%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
∈ S and v = ![\left[\begin{array}{ccc}0\\1\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%5C%5C1%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
∈ S
As 1×1×0=0 0×1×1=0
But u+v = ![\left[\begin{array}{ccc}1+0\\1+1\\0+1\end{array}\right] =](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%2B0%5C%5C1%2B1%5C%5C0%2B1%5Cend%7Barray%7D%5Cright%5D%20%3D)
![\left[\begin{array}{ccc}1\\2\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C2%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
∉ S as 1×2×1 ≠ 0
Hence, it is not closed under addition.
Therefore; The set is not a subspace
Answer:
7) -3
8) B
Step-by-step explanation:
The answer is 3Е38, 30,000,000,000,000,000,000,000,000,000,000,000,000
Sketching the ladder and wall might help to make the question clearer. The ladder is represented by the hypotenuse of a right triangle and is opposite the 90-degree angle of this triangle. The opposite side of this triangle measures 12 feet. Thus, you have 2 of 3 sides in a right triangle: a 12-foot opposite side and a 15-foot hypotenuse. Can you now find the measure of the adjacent side, which is the distance the base of the ladder is located away from the base of the wall? The Pythagorean Theorem would be the easiest approach to use here, but you could also solve this problem using trig.
