Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 20
Question A 20 

If A is a matrix with 5 rows and 4 columns such that the set of solutions to the homogeneous system has 2 parameters, what is the rank of ? 
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Hint 

Consider the RankNullity Theorem. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The set of solutions to the homogeneous system has parameters, so the dimension of the null space of this matrix is . The dimension of the domain is . By the RankNullity Theorem, we have . Thus, the rank of is . 