Question

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

Answer 1

the answer is C

Explanation:

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Answer 2

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]`

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]`