(a) For the given matrix, the transformation is not one to one
(b) For the given matrix the transformation is one to one.
(a) Let us consider the following matrix:
A = [ 1 8 2
0 1 -4
0 0 0 ]
The two roes of A is linearly independently.
The rank of the matrix is 2
rank (T) = 2
The domain is R³
dim domain(T) = 3
therefore,
nullity (T) = dim domain(T) - rank(T)
= 3 - 2
= 1
Hence the transformation is not one to one.
(b) Let us consider the following matrix:
A = [ 1 4 2
0 1 9
0 0 1 ]
The three rows of B is linearly independently.
The rank of the matrix is 3
rank (T) = 3
The domain is R³
dim domain(T) = 3
therefore,
nullity (T) = dim domain(T) - rank(T)
= 3 - 3
= 0
Hence the transformation is one to one.
Hence we prove the following matices.
Learn more about Matrices here:
brainly.com/question/11989522
#SPJ4