Question

Write the system of equations associated with each augmented matrix . Do not solve. [10020103001−2]\left[ \begin{matrix} 
1 & 0 & 0 & 2 \ 
0 & 1 & 0 & 3 \ 
0 & 0 & 1 & -2 
\end{matrix} ight]

Accepted Answer

Identify the number of variables in the system by counting the number of columns in the coefficient part of the augmented matrix (excluding the last column which represents the constants). For a 4x3 matrix, typically the first two columns are coefficients and the last column is constants, so confirm the exact structure given. Label the variables as $$x$$, $$y$$, and $$z (or as $$many variables as there are columns minus one). For example, if the matrix has 3 columns, then there are 2 variables and 1 column for constants; if it has 4 columns, then 3 variables and 1 column for constants. Write each row of the matrix as an equation by multiplying each coefficient by its corresponding variable and setting the sum equal to the constant in the last column. For example, if the first row is $$[a_{11}, a_{12}, a_{13}, b_1$]$$, write the equation as $$a_{11}x$$ + $$a_{12}y$$ + $$a_{13}z$$ = $$b_1. $$Repeat this process for each row of the matrix, resulting in a system of linear equations where each equation corresponds to a row in the matrix. Present the system of equations clearly, listing each equation on a separate line, without solving them as per the problem instructions.

Write the system of equations associated with each augmented matrix . Do not solve.
$[\begin{matrix} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & - 2 \end{matrix}]$

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Key Concepts

Augmented Matrix

System of Linear Equations

Matrix Dimensions and Variables

Write the system of equations associated with each augmented matrix . Do not solve. [10020103001−2]\(\left\)[ \(\begin{matrix}\) 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & -2 \(\end{matrix}\) \(\right\)]