# Problem Sheet 4 Null Spaces, Basis, Dimension-Linear Algebra-Assignment, Exercises for Linear Algebra. Institute of Mathematics and Applications

## Linear Algebra

Description: This course includes introduction and operation on matrices, Cramer rule, eigen values and eigen vector, complex matrices, LU factorization, linear system, vector operations, least square curves. This assignment of problems includes: Null, Space, Subspace, Basis, Dimension, Matrices, Real, Numbers, Nullity, System, Equations
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Problem Sheet # 4
1. Determine if the following sets are subspaces of ? If so, find basis and dimension.
i.      
ii.          
2. Determine if            is
subspace of ? If so, find basis and dimension of W.
3. Find null space of each the following matrices. Also find nullity and basis of each null
space.
i.
48542
13221
71163
ii.
20112
125448
121233
02215
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