Let B denote the reduced rowechelon form of A 5 3 1 7 9 0 2

Let B denote the reduced row-echelon form of A = (5 -3 -1 7 -9 0 2 -9 -5 3 1 -7) Find (a) B, and use it to find (b) the rank and nullity of A. (c) a basis for the nullspace of A. (d) a basis for the row space of A. (e) a basis for the column space of A.

Solution

for part a)

Make the pivot in the 1st column by dividing the 1st row by 5

Eliminate the 1st column

B )     Here Rank is 2   .Make the pivot in the 2nd column by dividing the 2nd row by -27/5

Divide the 1st row by 5

Multiply the 1st row by -9

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by -5

Subtract the 1st row from the 3rd row and restore it

Restore the 1st row to the original view

Calculate the number of linearly independent rows

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