The transformation is a reflection on the y-axis.
If we take the y-axis as the mirror line as shown in the diagram below, we can see that the distance of vertices A, B, and C to the mirror line are equals to the distance of vertices A', B' and C' to the mirror line.
Answer:
first one : x=−2y−5z−17
2nd one: x=
3
/2
y−z−8
3rd one: x=
−1
/3
y+
1
/3
z+1
Step-by-step explanation:
Answer:
8.48528137424^2
Step-by-step explanation:
8.48528137424x8.48528137424
= 72
Answer:
62 and 63
Step-by-step explanation:
125/2= 62.5 (Middle integer or mean of the 2 integers)
That means that the integers are 62 and 63
]Eigenvectors are found by the equation

implying that

. We then can write:
And:
Gives us the characteristic polynomial:

So, solving for each eigenvector subspace:
![\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]](https://tex.z-dn.net/?f=%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204%20%26%202%20%5C%5C%205%20%26%201%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20x%20%5C%5C%20y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20-x%20%5C%5C%20-y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20)
Gives us the system of equations:
Producing the subspace along the line

We can see then that 3 is the answer.