Given the following matrix A: A = Matrix 6 2 6 4 1 7 1 0 3 3 4 7 7 0 9 7 4 2 0 8

Question

Given the following matrix A:
A =
Matrix 6 2 6 4 1 7
1 0 3 3 4 7
7 0 9 7 4 2
0 8 0 7 6 6
1 8 3 10 10 13

and its row reduced echelon form:
rref(A) =
Matrix 1 0 0 0 -13/7 -31/4
0 1 0 0 1/2 6
0 0 1 0 5/3 131/12
0 0 0 1 2/7 -6
0 0 0 0 0 0

(a) Find a basis for the row space of A.
(b) Find a basis for the column space of A.
(c) Find a basis for the null space of A.
(d) What is the rank of this matrix A?
(e) What is the nullity of this matrix A?
(f) Find a basis for the null space of A ^T.
(g) In a smart way, determine a basis for the column space A^ T.

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Explanation / Answer

rank of a matrix is the no of non zero rows in the rows reduced echlon form thus rank of A=4

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