Matrix-Vector Form Write an Augmented Matrix

[cosmos42]

Homework Statement

Write in Vector-Matrix form then write the augmented matrix of the system.
r + 2s + t = 1
r - 3s +3t = 1
4s - 5t = 3

Homework Equations

The matrix to which the operations will be applied is called the augmented matrix of the system Ax = b, It is formed by appending the entries of the column vector b (right hand side of the equation) to those of the coefficient matrix A, creating a matrix that is now of order m x (n + 1).

The Attempt at a Solution

I know to use the coefficients to build the rows and columns of a 3 x 3 (?) matrix but I don't understand the augmentation part.

 

[Mark44]

Homework Statement

Write in Vector-Matrix form then write the augmented matrix of the system.
r + 2s + t = 1
r - 3s +3t = 1
4s - 5t = 3

Homework Equations

The matrix to which the operations will be applied is called the augmented matrix of the system Ax = b, It is formed by appending the entries of the column vector b (right hand side of the equation) to those of the coefficient matrix A, creating a matrix that is now of order m x (n + 1)^4.

The last bit makes no sense. If matrix A is m x n (m rows by n columns), the augmented matrix will be m x (n + 1), NOT m x (n + 1)^4.

The Attempt at a Solution

I know to use the coefficients to build the rows and columns of a 3 x 3 (?) matrix but I don't understand the augmentation part.

The constants on the right sides of the three equations will be the 4th column of the augmented 3 x 4 matrix.

 

[GadgetStrutter]

Okay, so you have these linear equations:

\begin{array}{lcl}
r + 2s + t & = & 1 \\
r - 3s + 3t & = & 1 \\
4s - 5t & = & 3 \end{array}​

Now, you said you know how to make them into a matrix. The augmentation part is actually really easy. All you have to do is add the answers to the last column.

\begin{array}{ccc}
1 & 2 & 1 & 1\\
1 & -3 & 3 & 1 \\
0 & 4 & -5 & 3\end{array}​

It is common to see a dotted line separating the fourth column from the 3x3 matrix.

 

[cosmos42]

The last bit makes no sense. If matrix A is m x n (m rows by n columns), the augmented matrix will be m x (n + 1), NOT m x (n + 1)^4.

The constants on the right sides of the three equations will be the 4th column of the augmented 3 x 4 matrix.

1.) THE 4 WAS A MISTAKE IT WAS AN INDEX FOR THE FOOTNOTE: "The optional vertical line between the entries of A and those of b emphasizes the way the matrix is constructed"

 

[cosmos42]

Okay, so you have these linear equations:

\begin{array}{lcl}
r + 2s + t & = & 1 \\
r - 3s + 3t & = & 1 \\
4s - 5t & = & 3 \end{array}​

Now, you said you know how to make them into a matrix. The augmentation part is actually really easy. All you have to do is add the answers to the last column.

\begin{array}{ccc}
1 & 2 & 1 & 1\\
1 & -3 & 3 & 1 \\
0 & 4 & -5 & 3\end{array}​

It is common to see a dotted line separating the fourth column from the 3x3 matrix.

Cool thanks!