Let psi M23 R right arrow M33R be the linear transformati

Let psi : M_2*3 (R ) right arrow M_3*3(R ) be the linear transformation give by psi(A) = (2 1 3 -1 2 1)A for every A element of M_2*3(R ). Find the dimension of ker(psi). Find the dimension of im(psi).

Solution

Using the property that dim(Ker A) + dim (Image A) = m

We will get the first condition as dim (Ker A) + dim ( Image A) = 3

The rows are not proportional, hence the dimesion of Image is equal to 2

Now using the above property we get

2 + dim(Ker A) = 3

dim (Ker A) = 1

(i) Answer is 1

(ii) Answer is 2