Question

1 The row-echelon reduced form of the matrix -22 3 1 3 2 0 2 0 0 -1 -1 0 1 -3 -2 2 is given by 10 0 10 2 R 0 10 0 1/2 -1/2 0 0 1 7 0 -5 Answer the following questions about A: Choose The nullity of A is: 3 Choo Let T be the linear transformation T:R → R given by T(x) = Ax. The number d is: Cha The number of free variables in the system of equations Ax = 0 is: C The number of pivots of A is:

Answer 1

a) the nullity of A^T is the number of rows in reduced row echelon form without leading entry 1.

here reduced row echelon form is R . it has leading entry in every row . so

Nullity (A^T) = 0

b) A m*n matrix represents transformation $\large T:\;R^n\rightarrow R^m$

here A is 3*6 . so this represents transformation $\large T:\;R^6\rightarrow R^3$

so d=6

c) number of free variables are number of columns without zero is reduced form of A.

here R has 3 columns with out leading entry 1. so

number of free variable= 3

d) we have 3 leading entry in reduced row echelon form of A . so

the number of pivot of A is 3