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egoroff_w [7]
3 years ago
13

Find the augmented matrix for each of the following systems of linear equations. (a) x₂ - 2x2 = 0 (6) x + x₃ = 1 .3x₂ + 4x2 = -1

- x₂ + 2x2x₃ = 3. 2x, - x₂ = 3 0 (c) x₂ + x3 =1 (d) x₂ = 1 2x₂ - x3 + x₂=2 X₂=2 2x3 + x4 = 3
Mathematics
2 answers:
Y_Kistochka [10]3 years ago
6 0

Answer:

The augmented matrix for each set of linear equations is:

a) x_1-2x_2=0\\3x_1+4x_2=-1\\2x_1-x_2=3

Augmented matrix:

\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right]

b) x_1+x_3=1\\-x_1+2x_2-x_3=3

Augmented matrix:

\left[\begin{array}{cccc}1&0&1&1\\-1&2&-1&3\end{array}\right]

c) x_1+x_3=1\\2x_2-x_3+x_5=2\\2x_3+x_4=3

Augmented matrix:

\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]

d) x_1=1\\x_2=2

Augmented matrix:

\left[\begin{array}{ccc}1&0&1\\0&1&2\end{array}\right]

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:  

\left[\begin{array}{cc}1&-2\\3&4\\2&-1\end{array}\right]

Then you have to make a vector with the constants in the linear equations, for the case of system a) the vector will be:  

\left[\begin{array}{c}0&-1&3\end{array}\right]

To construct the augmented matrix, you append those matrices together and create a new one:

\left[\begin{array}{ccc}1&-2&0\\3&4&-1\\2&-1&3\end{array}\right]

ikadub [295]3 years ago
5 0

Answer:

the answer is C

Step-by-step explanation:

i just did the assignment on  edge2020

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