Question

(a) Use Mathematica to find an echelon form of A.

(b) Using your answer to the previous part, find the rank and nullity of A.

(c) Find a basis for the row space of A.

(d) Find a basis for the column space of A.

(e) Find a basis for the null space of A.

(a) solution: reduced row space echelon form of A

(b) rank

nullity:

rankA + nullityA = number of columns of A.

therefore, nullityA= no. of columnsA - rankA = 5-3 =2

(c) row space of A

(d) column space of A

(e) null space of A

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