Write the augmented matrix for each system of linear equations...

Question

Write the augmented matrix for each system of linear equations.

$\begin{cases}5x - 2y - 3z = 0 \x + y = 5 \2x - 3z = 4\end{cases}$

Accepted Answer

hey everyone here we are asked to determine the augmented matrix that corresponds to the given system of equations. So our first given equation is x plus four, Y is equal to seven. Our second equation is negative four, X minus five, Y is equal to two. And our third and final equation is negative two, X minus seven. And why plus the is equal to negative eight. So now our first step here in solving this problem is to show the coefficient of each variable. So beginning with our first equation, we see that we have X all on its own. When we know that when a variable is on its own, the one coefficient is implied. So we can include this coefficient. So we have one X. And then just the plus four Y. Well we have X and y but we are missing the Z variable which tells us that in this equation the coefficient of Z is zero. So to this equation we can just add zero Z. And then this equation is equal to seven. Now we can move on to our second equation where we have negative four, X minus five, Y again is equal to two. And here, once again we have X and y but we are missing Z. So we can just add plus zero Z. And now we're all done here, we can move on to our third equation where we have negative two x minus seven, Y. And we have a Z term here all on its own. So we can just add the one coefficient as we did before. So we have plus one, Z is equal to negative eight. So now that we have clearly identified each of these coefficients for each variable. We can go ahead and start writing our augmented matrix. So if we recall for an augmented matrix it has a vertical line here to represent the equal sign into the left hand side, we place the coefficients for each given variable. So going from left to right, our columns will be the X coefficients, then Y and then the z coefficients from each equation. And to the right hand side of the bar we have all of the constants. So now we can start filling in our matrix. Starting with our first equation for our first row we see we have the values one for x. Then we moved to four for y and then zero for our z coefficient. Then we have is equal to seven which we place on the right hand side of the bar. Now we can move on to our second row for the second equation and we have the values negative four, negative five and zero. And then on the right hand side we have is equal to two. So we place the number two. Now we can move on to our final equation which has the values negative two negative 71 and negative eight for our final role. And now with this we have completed filling in our augmented matrix and this leaves us with answer choice B. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Write the augmented matrix for each system of linear equations.
$\begin{cases}\)5x - 2y - 3z = 0 \\(\x\) + y = 5 \\2x - 3z = 4\(\end{cases}$

Key Concepts

System of Linear Equations

Augmented Matrix

Matrix Representation of Equations

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