Answer:
The augmented matrix for each set of linear equations is:
a) [tex]x_1-2x_2=0\\3x_1+4x_2=-1\\2x_1-x_2=3[/tex]
Augmented matrix:
[tex]\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right][/tex]
b) [tex]x_1+x_3=1\\-x_1+2x_2-x_3=3[/tex]
Augmented matrix:
[tex]\left[\begin{array}{cccc}1&0&1&1\\-1&2&-1&3\end{array}\right][/tex]
c) [tex]x_1+x_3=1\\2x_2-x_3+x_5=2\\2x_3+x_4=3[/tex]
Augmented matrix:
[tex]\left[\begin{array}{cccccc}1&0&1&0&0&1\\0&2&-1&0&1&2\\0&0&2&1&0&3\end{array}\right][/tex]
d) [tex]x_1=1\\x_2=2[/tex]
Augmented matrix:
[tex]\left[\begin{array}{ccc}1&0&1\\0&1&2\end{array}\right][/tex]
Step-by-step explanation:
In order to find the augmented matrix, you have to take the numeric values of each variable and make a matrix with them. For example, in the linear system a) you can make a matrix out of the numeric values accompanying x_1 and x_2, this matrix will be:
[tex]\left[\begin{array}{cc}1&-2\\3&4\\2&-1\end{array}\right][/tex]
Then you have to make a vector with the constants in the linear equations, for the case of system a) the vector will be:
[tex]\left[\begin{array}{c}0&-1&3\end{array}\right][/tex]
To construct the augmented matrix, you append those matrices together and create a new one:
[tex]\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right][/tex]
Answer:
the answer is C
Step-by-step explanation:
i just did the assignment on edge2020
