MATH 310
Self-quiz 25
1. Find the null space of the matrix:
1 2 1
2 1 0
2. Find the rank of the matrix:
1 2 −2
2 1 1
1−1 3
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Solved Quiz 25 - 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 25
- Find the null space of the matrix:
- Find the rank of the matrix:
MATH 310
Self-quiz 25
- Find the null space of the matrix:
Solution: The null-space of this matrix consists of all the vectors (x, y, z)T which are such that:
x y z
In other words, we need to solve the system with augmented matrix:
We will use the Gauss-Jordan elimination method:
) − 2 R 1 + R 2
R 2
If we go back to our variables we find:
3 R 2 + R 3
5 3 C^2 +^ C^3
This last matrix has obviously rank 2 and this is also the rank of the initial matrix.