Answer: hello some part of your question is missing
Let v=〈−2,5〉 in R^2,and let y=〈0,3,−2〉 in R^3.
Find a unit vector u in R^2 such that u is perpendicular to v. How many such vectors are there?
answer:
One(1) unit vector ( < 5/√29, 2 /√29 > ) perpendicular to 〈−2,5〉
Step-by-step explanation:
let
u = < x , y > ∈/R^2 be perpendicular to v = < -2, 5 > ------ ( 1 )
hence :
-2x + 5y = 0
-2x = -5y
x = 5/2 y
back to equation 1
u = < 5/2y, y >
∴ || u || = y/2 √29
∧
u = < 5 /2 y * 2 / y√29 , y*2 / y√29 >
= < 5/√29, 2 /√29 > ( unit vector perpendicular to < -2, 5 > )
Answer:0
Step-by-step explanation:
- 0/12x
x=0
The first even multiple of 9 is 18.
Answer:
![x\ =\ \dfrac{209}{30}](https://tex.z-dn.net/?f=x%5C%20%3D%5C%20%5Cdfrac%7B209%7D%7B30%7D)
![y\ =\ \dfrac{29}{18}](https://tex.z-dn.net/?f=y%5C%20%3D%5C%20%5Cdfrac%7B29%7D%7B18%7D)
![z\ =\ \dfrac{64}{15}](https://tex.z-dn.net/?f=z%5C%20%3D%5C%20%5Cdfrac%7B64%7D%7B15%7D)
Step-by-step explanation:
Given equations are
15x + 15y + 10z = 106
5x + 15y + 25z = 135
15x + 10y - 5z = 42
The augmented matrix by using above equations can be written as
![R_1\ \rightarrow\ \dfrac{R_1}{15}](https://tex.z-dn.net/?f=R_1%5C%20%5Crightarrow%5C%20%5Cdfrac%7BR_1%7D%7B15%7D)
![=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\5&15&25|135\\15&15&-5|42\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%26%5Cdfrac%7B10%7D%7B15%7D%7C%5Cdfrac%7B106%7D%7B15%7D%5C%5C5%2615%2625%7C135%5C%5C15%2615%26-5%7C42%5Cend%7Barray%7D%5Cright%5D)
![R_1\rightarrowR_2-5R1\ and\ R_3\rightarrow\ R_3-15R_1](https://tex.z-dn.net/?f=R_1%5CrightarrowR_2-5R1%5C%20and%5C%20R_3%5Crightarrow%5C%20R_3-15R_1)
![=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\\\0&10&\dfrac{65}{3}|\dfrac{299}{3}\\\\0&0&-15|-64\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%26%5Cdfrac%7B10%7D%7B15%7D%7C%5Cdfrac%7B106%7D%7B15%7D%5C%5C%5C%5C0%2610%26%5Cdfrac%7B65%7D%7B3%7D%7C%5Cdfrac%7B299%7D%7B3%7D%5C%5C%5C%5C0%260%26-15%7C-64%5Cend%7Barray%7D%5Cright%5D)
![R_2\rightarrow\ \dfrac{R_2}{10}](https://tex.z-dn.net/?f=R_2%5Crightarrow%5C%20%5Cdfrac%7BR_2%7D%7B10%7D)
![=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&-15|-64\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%26%5Cdfrac%7B10%7D%7B15%7D%7C%5Cdfrac%7B106%7D%7B15%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B65%7D%7B30%7D%7C%5Cdfrac%7B299%7D%7B30%7D%5C%5C%5C%5C0%260%26-15%7C-64%5Cend%7Barray%7D%5Cright%5D)
![R_3\rightarrow\ \dfrac{R_3}{-15}](https://tex.z-dn.net/?f=R_3%5Crightarrow%5C%20%5Cdfrac%7BR_3%7D%7B-15%7D)
![=\ \left[\begin{array}{ccc}1&1&\dfrac{10}{15}|\dfrac{106}{15}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&1|\dfrac{64}{15}\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%26%5Cdfrac%7B10%7D%7B15%7D%7C%5Cdfrac%7B106%7D%7B15%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B65%7D%7B30%7D%7C%5Cdfrac%7B299%7D%7B30%7D%5C%5C%5C%5C0%260%261%7C%5Cdfrac%7B64%7D%7B15%7D%5Cend%7Barray%7D%5Cright%5D)
![R_1\rightarrow\ R_1-R_2](https://tex.z-dn.net/?f=R_1%5Crightarrow%5C%20R_1-R_2)
![=\ \left[\begin{array}{ccc}1&0&\dfrac{-3}{2}|\dfrac{17}{30}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&1|\dfrac{64}{15}\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5Cdfrac%7B-3%7D%7B2%7D%7C%5Cdfrac%7B17%7D%7B30%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B65%7D%7B30%7D%7C%5Cdfrac%7B299%7D%7B30%7D%5C%5C%5C%5C0%260%261%7C%5Cdfrac%7B64%7D%7B15%7D%5Cend%7Barray%7D%5Cright%5D)
![R_1\rightarrow\ R_1+\dfrac{3}{2}R_3](https://tex.z-dn.net/?f=R_1%5Crightarrow%5C%20R_1%2B%5Cdfrac%7B3%7D%7B2%7DR_3)
![=\ \left[\begin{array}{ccc}1&0&0|\dfrac{209}{30}\\\\0&1&\dfrac{65}{30}|\dfrac{299}{30}\\\\0&0&1|\dfrac{64}{15}\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%7C%5Cdfrac%7B209%7D%7B30%7D%5C%5C%5C%5C0%261%26%5Cdfrac%7B65%7D%7B30%7D%7C%5Cdfrac%7B299%7D%7B30%7D%5C%5C%5C%5C0%260%261%7C%5Cdfrac%7B64%7D%7B15%7D%5Cend%7Barray%7D%5Cright%5D)
![R_2\rightarrow\ R_2-\dfrac{65}{30}R_3](https://tex.z-dn.net/?f=R_2%5Crightarrow%5C%20R_2-%5Cdfrac%7B65%7D%7B30%7DR_3)
![=\ \left[\begin{array}{ccc}1&0&\0|\dfrac{209}{30}\\\\0&1&0|\dfrac{29}{18}\\\\0&0&1|\dfrac{64}{15}\end{array}\right]](https://tex.z-dn.net/?f=%3D%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26%5C0%7C%5Cdfrac%7B209%7D%7B30%7D%5C%5C%5C%5C0%261%260%7C%5Cdfrac%7B29%7D%7B18%7D%5C%5C%5C%5C0%260%261%7C%5Cdfrac%7B64%7D%7B15%7D%5Cend%7Barray%7D%5Cright%5D)
Hence, we can write from augmented matrix,
![x\ =\ \dfrac{209}{30}](https://tex.z-dn.net/?f=x%5C%20%3D%5C%20%5Cdfrac%7B209%7D%7B30%7D)
![y\ =\ \dfrac{29}{18}](https://tex.z-dn.net/?f=y%5C%20%3D%5C%20%5Cdfrac%7B29%7D%7B18%7D)
![z\ =\ \dfrac{64}{15}](https://tex.z-dn.net/?f=z%5C%20%3D%5C%20%5Cdfrac%7B64%7D%7B15%7D)