Question

Describe an example of an augmented matrix.

Answer 1

An augmented matrix refers to a matrix formed by appending the columns of two matrices.

The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.

If we have the system

`2x+3y=5\\x-4y=9`

The two maxtrix involved here are

`\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right]`

However, to solve the system using matrices, we have to formed an augmented matrix

`\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right]`

So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.

Answer 2

Explanation:

When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.

Let A=
`\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right]`

B=
`\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]`

Then the augmented matrix is(A|B)

Note that a vertical line is used to separate te columns of A from the columns of B

(A|B)
`\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right]`

This is a simple example of augmented matrix....