Answer:
AB = ![\left[\begin{array}{ccc}-3&4&6\\-6&3&5\\5&0&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%264%266%5C%5C-6%263%265%5C%5C5%260%26-4%5Cend%7Barray%7D%5Cright%5D)
Each column of AB is written as a linear combination of columns of Matrix A in the explanation below.
Step-by-step explanation:
A = ![\left[\begin{array}{ccc}-2&2&1\\-3&1&1\\2&0&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%262%261%5C%5C-3%261%261%5C%5C2%260%26-1%5Cend%7Barray%7D%5Cright%5D)
B= ![\left[\begin{array}{ccc}2&-1&0\\1&2&1\\-1&-2&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-1%260%5C%5C1%262%261%5C%5C-1%26-2%264%5Cend%7Barray%7D%5Cright%5D)
We need to write each column of AB as a linear combination of the columns of A so we will multiply each column of A with each column element of B to get the column of AB. So,
AB Column 1 = 2 *
+ 1
+ (-1)
= ![\left[\begin{array}{ccc}-3\\-6\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%5C%5C-6%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
AB Column 2 = (-1)
+ 2
+ (-2)
= ![\left[\begin{array}{ccc}4\\3\\0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C3%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
AB Column 3 = (0)
+ (1)
+ 4
= ![\left[\begin{array}{ccc}6\\5\\-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C5%5C%5C-4%5Cend%7Barray%7D%5Cright%5D)
Finally, we can combine all three columns of AB to form the 3x3 matrix AB.
AB = ![\left[\begin{array}{ccc}-3&4&6\\-6&3&5\\5&0&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%264%266%5C%5C-6%263%265%5C%5C5%260%26-4%5Cend%7Barray%7D%5Cright%5D)
Answer:
B
Step-by-step explanation:
Because 9 = 5 +4
Answer:
![$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D0.73%24)
Step-by-step explanation:
The identity you will use is:
![$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28x%5Cright%29%3D%5Cfrac%7B1%7D%7B%5Csin%20%5Cleft%28x%5Cright%29%7D%24)
So,
![$\csc \left(\theta-\frac{\pi }{2}\right)$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%24)
![$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B%5Csin%20%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2B%5Ctheta%5Cright%29%7D%24)
Now, using the difference of sin
Note: state that ![\text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)](https://tex.z-dn.net/?f=%5Ctext%7Bsin%7D%28%5Calpha%5Cpm%20%5Cbeta%29%3D%5Ctext%7Bsin%7D%28%5Calpha%29%20%5Ctext%7Bcos%7D%28%5Cbeta%29%20%5Cpm%20%5Ctext%7Bcos%7D%28%5Calpha%29%20%5Ctext%7Bsin%7D%28%5Cbeta%29)
![$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B-%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%2B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%5Csin%20%5Cleft%28%5Ctheta%5Cright%29%7D%24)
Solving the difference of sin:
![$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$](https://tex.z-dn.net/?f=%24-%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%2B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%5Csin%20%5Cleft%28%5Ctheta%5Cright%29%24)
![-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)](https://tex.z-dn.net/?f=-%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%20%5Ccdot%201%2B0%5Ccdot%20%5Csin%20%5Cleft%28%5Ctheta%5Cright%29)
![-\text{cos} \left(\theta\right)](https://tex.z-dn.net/?f=-%5Ctext%7Bcos%7D%20%5Cleft%28%5Ctheta%5Cright%29)
Then,
![$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%24)
Once
![\text{sec}(-\theta)=\text{sec}(\theta)](https://tex.z-dn.net/?f=%5Ctext%7Bsec%7D%28-%5Ctheta%29%3D%5Ctext%7Bsec%7D%28%5Ctheta%29)
And,
![$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$](https://tex.z-dn.net/?f=%24-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%3D-%5Ctext%7Bsec%7D%28%5Ctheta%29%24)
![$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$](https://tex.z-dn.net/?f=%24-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%3D-%28-0.73%29%24)
![$-\frac{1}{\cos \left(\theta\right)}=0.73$](https://tex.z-dn.net/?f=%24-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%3D0.73%24)
Therefore,
![$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D0.73%24)
Answer:
-5 x (4-n)
Step-by-step explanation:
Answer:
It is a right triangle
Step-by-step explanation:
Depending on how you make the triangle if 3 is A 4 is B and 5 is C then the Pythagorean Theorm would be correct and it would be a right triangle.