Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 09
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Question A 09 

For questions A9 and A10 below, consider the homogeneous system of equations represented by this augmented matrix in reduced row echelon form:
(9) What is the rank of the augmented matrix above? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Observe that the given augmented matrix is already in reduced row echelon form. How rank of a matrix is related to its reduced row echelon form? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that the rank of a matrix is the number of leading entries (or the number of nonzero rows) in a row reduced form of the matrix. As we see the Hint, the given augmented matrix is already in the reduced row echelon form. By counting the number of leading entries, the rank is . 