Answer:
a) The set of solutions is 
y b) the set of solutions is 
.
Step-by-step explanation:
a) Let's first find the echelon form of the matrix ![\left[\begin{array}{ccc}5&2&6\\-2&1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%262%266%5C%5C-2%261%263%5Cend%7Barray%7D%5Cright%5D)
.
- We add
from row 1 to row 2 and we obtain the matrix ![\left[\begin{array}{ccc}5&2&6\\0&\frac{9}{5} &\frac{27}{5}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%262%266%5C%5C0%26%5Cfrac%7B9%7D%7B5%7D%20%26%5Cfrac%7B27%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
- From the previous matrix, we multiply row 1 by
and the row 2 by 
and we obtain the matrix ![\left[\begin{array}{ccc}1&\frac{2}{5} &\frac{6}{5} \\0&1&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%5Cfrac%7B2%7D%7B5%7D%20%26%5Cfrac%7B6%7D%7B5%7D%20%5C%5C0%261%263%5Cend%7Barray%7D%5Cright%5D)
. This matrix is the echelon form of the initial matrix.
The system has a free variable (x3).
- 0=x1+x2+
x3=
x1+(-3x3)+x3=
x1-x3+x3
then x1=0.
The system has infinite solutions of the form (x1,x2,x3)=(0,-3x3,x3), where x3 is a real number.
b) Let's first find the echelon form of the aumented matrix ![\left[\begin{array}{ccccc}1&-2&1&-4&1\\1&3&7&2&2\\0&-12&-11&-16&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%26-2%261%26-4%261%5C%5C1%263%267%262%262%5C%5C0%26-12%26-11%26-16%265%5Cend%7Barray%7D%5Cright%5D)
.
- To row 2 we subtract row 1 and we obtain the matrix
![\left[\begin{array}{ccccc}1&-2&1&-4&1\\0&5&6&6&1\\0&-12&-11&-16&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%26-2%261%26-4%261%5C%5C0%265%266%266%261%5C%5C0%26-12%26-11%26-16%265%5Cend%7Barray%7D%5Cright%5D)
- From the previous matrix, we add to row 3,
of row 2 and we obtain the matrix ![\left[\begin{array}{ccccc}1&-2&1&-4&1\\0&5&6&6&1\\0&0&\frac{17}{5}&\frac{-8}{5}&\frac{37}{5} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%26-2%261%26-4%261%5C%5C0%265%266%266%261%5C%5C0%260%26%5Cfrac%7B17%7D%7B5%7D%26%5Cfrac%7B-8%7D%7B5%7D%26%5Cfrac%7B37%7D%7B5%7D%20%20%20%5Cend%7Barray%7D%5Cright%5D)
.
- From the previous matrix, we multiply row 2 by and the row 3 by
and we obtain the matrix ![\left[\begin{array}{ccccc}1&-2&1&-4&1\\0&1&\frac{6}{5} &\frac{6}{5}&\frac{1}{5}\\0&0&1&\frac{-8}{17}&\frac{37}{17} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%26-2%261%26-4%261%5C%5C0%261%26%5Cfrac%7B6%7D%7B5%7D%20%26%5Cfrac%7B6%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C0%260%261%26%5Cfrac%7B-8%7D%7B17%7D%26%5Cfrac%7B37%7D%7B17%7D%20%5Cend%7Barray%7D%5Cright%5D)
. This matrix is the echelon form of the initial matrix.
The system has a free variable (x4).
- x3-
x4=
, then x3=+ ![\frac{8}{17}x4.x2+[tex]\frac{6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B17%7Dx4.%3C%2Fli%3E%3C%2Ful%3E%3Cul%3E%3Cli%3Ex2%2B%5Btex%5D%5Cfrac%7B6%7D%7B5%7D)
x3+x4=, x2+(+![\frac{8}{17}x4)+[tex]\frac{6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B17%7Dx4%29%2B%5Btex%5D%5Cfrac%7B6%7D%7B5%7D)
x4=, then
x2=
x4.
- x1-2x2+x3-4x4=1, x1+
+
x4++x4-4x4=1, then x1=
The system has infinite solutions of the form (x1,x2,x3,x4)=(-6,x4,+ x4,x4), where x4 is a real number.
Answer:
communitive property of addition
Step-by-step explanation:
The community property of addition states: a+b=b+a
This basically means that when you add two numbers, the order of when you add them does not occur.
Answer:
They both have 12, 24, and 48 in common
Step-by-step explanation:
Basically you just look at the multiples of the two numbers and look for the one that are the same.
Hope it right and have a great day! :)
Answer:
Step-by-step explanation:
