MATH 310
Self-quiz 31
1. Find the inverse of the matrix:
1 2 −1
2 5 1
3 1 1
2. Find the rank and the nullity of the matrix:
1 2 −1
2 1 1
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Quiz 31 with Solutions - Applied Linear Algebra | MATH 310, Quizzes of Linear Algebra
Material Type: Quiz; Class: Applied Linear Algebra; Subject: Mathematics; University: University of Illinois - Chicago; Term: Unknown 2012;
Typology: Quizzes
2011/2012
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MATH 310
Self-quiz 31
- Find the inverse of the matrix:
- Find the rank and the nullity of the matrix:
MATH 310
Self-quiz 31
- Find the inverse of the matrix:
Solution: We will use the Gauss Jordan method in order to bring the matrix:
in reduced row echelon form:
− 2 R 1 + R 2
− 3 R 1 + R 3
5 R 2 + R 3
1 19 R^3
− 3 R 3 + R 2
R 3 + R 1
) C 2 + C 3
From the above form, it follows immediately that the rank of the matrix is
- This implies that its nullity is 1.