the coefficients of the unknown variable $$ d $$ were put in column 1 the coefficients of the unknown variable $$ r $$ were put in column 2 the coefficients of the unknown variable $$ a $$ were put in column 3 which was row reduced to: $$ \left[\begin{array}{llll}1 & 0 & 0 & -5 \ 0 & 1 & 0 & 1 \ 0 & 0 & 1 & 2\end{array} ight] $$ What is the solution to the original system of equations? $$ a=\square $$ $$ d=\square $$

Question

the coefficients of the unknown variable $$ d $$ were put in column 1 the coefficients of the unknown variable $$ r $$ were put in column 2 the coefficients of the unknown variable $$ a $$ were put in column 3 which was row reduced to: $$ \left[\begin{array}{llll}1 & 0 & 0 & -5 \ 0 & 1 & 0 & 1 \ 0 & 0 & 1 & 2\end{array}ight] $$ What is the solution to the original system of equations? $$ a=\square $$ $$ d=\square $$

UpStudy AI · Accepted Answer

The row-reduced form of the matrix you provided is:

$$
\left[\begin{array}{ccc|c} 
1 & 0 & 0 & -5 \ 
0 & 1 & 0 & 1 \ 
0 & 0 & 1 & 2 
\end{array}\right]
$$

This corresponds to the following system of equations:

1. $$ d = -5 $$
2. $$ r = 1 $$
3. $$ a = 2 $$

From this, we can directly read off the values of the unknown variables:

- $$ d = -5 $$
- $$ r = 1 $$
- $$ a = 2 $$

Thus, the solution to the original system of equations is:

$$
a = 2
$$
$$
d = -5
$$
$$ a = 2 $$ $$ d = -5 $$

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