Answer:
3.6000
Step-by-step explanation:
I did this three different ways I think this is right.
Answer:
∠A= 60°
Step-by-step explanation:
Answer:
I can't sorry i wish I could help but I can't.
Step-by-step explanation:
sorry.
The question is missing. Here is the complete question.
Let y =
and u =
. Write y as the sum of a vector in Span(u) and a vector orthogonal to u.
Answer: y = ![\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%20%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B-1%7D%7B10%7D%5C%5C%20%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation: The sum of vectors is given by
y =
+ z
where
is in Span(u);
vector z is orthogonal to it;
First you have to compute the orthogonal projection
of y:
= proj y = 
Calculating orthogonal projection:
.
= ![\left[\begin{array}{c}9\\6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%5C%5C6%5Cend%7Barray%7D%5Cright%5D)
.
= ![\left[\begin{array}{c}49\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D49%5C%5C1%5Cend%7Barray%7D%5Cright%5D)



![y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right]](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cfrac%7B3%7D%7B10%7D.%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]](https://tex.z-dn.net/?f=y_%7B1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Calculating vector z:
z = y - 
z = ![\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C6%5Cend%7Barray%7D%5Cright%5D%20-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
z = ![\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-1%7D%7B10%7D%20%5C%5C%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
Writing y as the sum:
![y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right]](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B21%7D%7B10%7D%20%5C%5C%5Cfrac%7B3%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-1%7D%7B10%7D%20%5C%5C%5Cfrac%7B57%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
B. 20 (do 78 divided by 3.75 (3 3/4) and that equals 20.8)