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TRENTO, A.A. 2019/20

MATHEMATICS FOR DATA SCIENCE/BIOSTATISTICS EXERCISE SHEET # 6

Important! In solving the exercises

• explain what you are doing,

• explain why you are doing what you are doing, and

• spell out all intermediate steps.

Exercise 6.1. For all the linear systems having solutions in the Exercises 5.1 - 5.9

• find the rank of A;

• find the nullity of A;

• find a basis of the nullspace of A.

Exercise 6.2. Let V be the vector space of the 2× 2 real matrices.

We recall that dim(V ) = 4.

Are the matrices A =

[ 0 1 2 3

]

, B =

[ 1 2 3 0

]

, C =

[ 1 0 0 0

] , a basis of V ?

Exercise 6.3. Let V be the vector space of the 2× 2 real matrices.

Are the matrices A =

[ 0 1 2 3

]

, B =

[ 1 2 3 0

]

, C =

[ 1 0 0 0

]

, D =

[ 0 1 0 0

] , a basis of V ?

Exercise 6.4. Let V be the vector space of the 2× 2 real matrices.

Are the matrices A =

[ 0 1 2 3

]

, B =

[ 1 2 3 0

]

, C =

[ 1 3 3 0

]

, D =

[ 0 1 0 0

] , a basis of V ?

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