Write the system of equations associated with each augmented matrix . Do not solve.

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Hey, everyone. Here we are asked to find the system of equations associated with the given augmented matrix. Here, our given augmented matrix has three rows and four columns. The first row contains the values 370 and nine. The second row contains the values 065 and 13. And the third row contains the values 209 and eight. Here we have four answer choice options, answer choices A through D each being a system of three equations with the variables X Y and Z. So here looking at our given augmented matrix first, we need to recall that the vertical line in this matrix represents an equal sign. And then the column to the right of this vertical line are the values of the constants and each row individually is one equation. So here we have three rows which tells us we will have three different equations. And then we, we have three columns to the left of our vertical line. So this tells us that we have three variables and looking at our solutions, we know these variables are X Y and Z. So going in alphabetical order, the left most column it will be the coefficient of X. The second column will be the coefficient of Y and the third column will be the coefficient of Z. So now with each variable column identified as well as the other information provided here, we can write our three equations as a system of equations. So beginning with our first row here, we see we have three in the X column. So we have three times X plus, then seven times Y plus zero times Z is equal to the constant value here, which is nine. Now just cleaning up this equation here, we have one equation of three, X plus seven, Y is equal to nine. Now, moving on to our second row, we have our second equation here of zero times X plus six times Y plus five times Z is equal to 13. Now cleaning up this expression here, we have six, Y plus five, Z is equal to 13. So we have found our second simplified equation. And now looking at the third row, we get our third equation which is two times X plus zero times Y plus nine times Z is equal to eight. Cleaning up this expression, we have two X plus nine Z is equal to A. So now just summarizing each of our simplified equations here, we have a total of three equations for each of our rows here. So we have three X plus seven, Y is equal to nine. Then we have six Y plus five, Z is equal to 13. And our third and last equation is two X plus nine, Z is equal to eight. So with our three equations here we are left with answer choice. A where again, our first equation is three X plus seven, Y is equal to nine. And then our second equation is six, Y plus five, Z is equal to 13. And our third equation is two X plus nine, Z is equal to eight. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Write the system of equations associated with each augmented matrix . Do not solve.

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Key Concepts

Augmented Matrix

System of Linear Equations

Writing Equations from Matrices