Questions: Write an augmented matrix for the following system of equations. x-7y+z= -3 6x-8y+6z= 1 5y-4z= -2 The entries in the matrix are:

Transcript text: Question 41 of Write an augmented matrix for the following system of equations. \[ \begin{aligned} x-7 y+z= & -3 \\ 6 x-8 y+6 z= & 1 \\ 5 y-4 z= & -2 \end{aligned} \] The entries in the matrix are: $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$ $\square$

Solution

Solution Steps

Step 1: Identify the coefficients and constants

The given system of equations is: \[ \begin{aligned} x - 7y + z &= -3 \\ 6x - 8y + 6z &= 1 \\ 5y - 4z &= -2 \end{aligned} \]

We can extract the coefficients of $x$, $y$, and $z$ along with the constants on the right-hand side of each equation.

Step 2: Construct the augmented matrix

The augmented matrix is formed by placing the coefficients of the variables and the constants in a matrix format. Each row corresponds to one equation, and each column corresponds to one variable (or the constant term).

The augmented matrix for the given system is: \[ \begin{bmatrix} 1 & -7 & 1 & | & -3 \\ 6 & -8 & 6 & | & 1 \\ 0 & 5 & -4 & | & -2 \end{bmatrix} \]