Write the system of linear equations represented by the augmen...

Question

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.

$\begin{bmatrix}5 & 0 & 3 & \vert & -11 \0 & 1 & -4 & \vert & 12 \7 & 2 & 0 & \vert & 3\end{bmatrix}$

Accepted Answer

hey everyone here we are asked to determine the system of linear equations associated to the given augmented matrix. So first hour given augmented matrix has three rows. The first row has values of zero to negative five and eight. Our second row has values of one, set 70 and 15. And our final third row has the values 90, negative three and four. So here first we need to recall that for an augmented matrix. We have this vertical line here and this vertical line represents an equal sign in the system of equations. And so to the right, these values are all constants and to the left, all of these terms are actually coefficients of the variables from the equations. So we're told to use variables X, Y, N. Z. So going from left to right, we have coefficients of X, then Y and finally Z. So with this information we can look at each row and get our three equations. So from our first row we have zero for the coefficient of X. We then have plus two, Y Then -5, Z Is equal to eight. And now we can move on to the second row and get our second equation. So we have one X plus seven, Y Plus zero, Z is equal to 15. And then finally moving on to the third row for our third equation, we have nine, X plus zero, y minus three, Z is equal to four. And now all that is left to do is to make some quick simplifications so we can go ahead and get rid of all terms with a zero coefficient because they will just be zero. And then we can also get rid of coefficients of one since a one is already implied when we have a variable that is on its own. So doing this, we can again begin at our first equation here, so we can just get rid of the zero X. And we are left with with two y minus five, Z is equal to eight. And now moving on to our second equation, we have this one X, which is just X. So we have X. And we can also get rid of the zero Z. So we are left with X plus seven, Y is equal to 15. And now moving on to our final equation. All we have to do here is get rid of the zero Y. And we are left with nine x minus three, Z is equal to four. And so with this we have finished our system of equations and we are left with answer choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.
$\begin{bmatrix}\)5 & 0 & 3 & \(\vert\) & -11 \\0 & 1 & -4 & \(\vert\) & 12 \\7 & 2 & 0 & \(\vert\) & 3\(\end{bmatrix}$

Key Concepts

Augmented Matrix Representation

Writing Systems of Linear Equations from Matrices

Variables and Their Order

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