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

Question

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

Accepted Answer

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. For the first row, we have the values 475 and three. For the second row, we have the values 37 76 and 19. And for the third row, we have the values negative five, negative 74 and 31. Here we have four answer choice options, answer choices A through D. Each of them being a system of three equations including the variables Xy and Z. Looking back at our given augmented matrix here we first need to recall that the vertical line represents an equal sign. The column to the right of the vertical line are the values for the constants for each equation. And we also need to note that each row will give its own equation. And now looking at our possible solutions, we notice that the variables we are dealing with are XY and Z. So going from alphabetical order from the first column, the leftmost column to the third column, we begin with the first column as our X coefficients. Then the second column are our Y coefficients and the third column are our Z coefficients. So now with each column properly identified here, we can begin writing out our three different equations, one for each row. So beginning with our first row, we see that the value in the X column is four. So we have a coefficient of four giving us four X moving on to Y, we have a coefficient of seven. So we have plus seven Y, we then have our Z coefficient uh as five. So we have plus five Z and then we have the vertical line. So we know that this expression is equal to the value on the right side which is three, repeating this process. For the last two rows, we have our second equation from our second row as three X plus seven, Y plus six, Z is equal to 19. And from our third row, we have the values negative five X minus seven, Y plus four, Z is equal to 31. And since we are not asked to solve our system of equations, these three equations serve as our solution here. So with these three equations, we are left here with answer choice B where again, we have a system of three equations. The first equation is four, X plus seven, Y plus five, Z is equal to three. The second equation is three X plus seven, Y plus six, Z is equal to 19. And our third equation is negative five X minus seven Y plus four Z is equal to 31. 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. <4x3 Matrix>

Verified Solution

Key Concepts

Augmented Matrix

System of Linear Equations

Translating Matrices to Equations