SOLUTION: Hi! I need help with "row operations". From what I have researched and studied, I understand that "row operations" are like matrices.
The question I have is as follows:
"Consid
Algebra ->
Matrices-and-determiminant
-> SOLUTION: Hi! I need help with "row operations". From what I have researched and studied, I understand that "row operations" are like matrices.
The question I have is as follows:
"Consid
Log On
Question 846921: Hi! I need help with "row operations". From what I have researched and studied, I understand that "row operations" are like matrices.
The question I have is as follows:
"Consider the system of equations
x - 4y = -5
-3x + 5y = 1
Using "row operations" find the exact answer for (x,y). Make sure you show intermediate steps."
All I have been able to do so far is put the system of equations in to a matrices form.
1 -4 | x = -5
-3 5 | y = 1
I don't understand what I am meant to do next. The examples we get are a lot easier than this and so I cannot seem to apply the easy examples to this example. I cannot get any numbers to be 0 or 1. They just keep getting bigger and bigger.
Please help!!!
Zeedee
You can put this solution on YOUR website! your solution is in the attached picture.
see below the picture for an explanation of what was done.
step 1 is your original equation.
step 2 creates your augmented matrix which includes the coefficients of the x and y terms plus the constant term on the right.
step 3 adds row 2 plus 3 * row 1 together and puts the result in row 2.
step 4 shows you the result after performing the operation in step 3.
the result of that operation is to make the number in column 1 row 2 equal to 0.
step 5 multiplies row 2 * -1/7 and puts the result in row 2.
step 6 shows you the result after performing the operation in step 5.
the result of that operation is to make the number in column 2 row 2 equal to 1.
step 7 adds row 1 + 4 * row 2 together and puts the result in row 1.
step 8 shows you the result of the operation in step 7.
the result of that operation is to make the number in column 2 row 1 equal to 0.
your matrix is now in the reduced form required by the gauss-jordan method.
all the coefficients are equal to 1.
row 1 has a coefficient of 1 in column 1 and a 0 in all other coefficient columns (only 2 columns in this problem).
row 2 has a coefficient of 1 in column 2 and a 0 in all other coefficient columns (only 2 columns in this problem).
once you get the matrix in this form, your solution is read off as:
x = 3
y = 2
you can confirm this solution is good by replacing x and y in the original equation and you'll see that both equations are true.
partickJMT goes fairly quickly, but his method is clear.
pause the video and you can even go back to wherever you want to start again by clicking on the video progress indicator bar, if you get lost or want to see parts of the video again.
the method is consistent to what I showed you, except that his example is a little more complex, which is good because you will eventually get to those more complex examples in your studies soon enough.
there is also a nice little calculator on the internet that you can use to check out your solution.
that calculator can be found at the following link:
