True or False: 7.) If T is one-to-one, then ker(T)={0vector}. 8.) If two real fi

ID: 2971276 • Letter: T

Question

True or False:

7.) If T is one-to-one, then ker(T)={0vector}.

8.) If two real finite dimensional vector spaces have the same dimension, they are isomorphic.

9.) If T: P2-->P2 is defined by T(p(x))=1+p(x), T is a linear transformation.

10.) If T: C[0,1]-->C[0,1] is given by T(f(x))=f(1), T is a linear transformation.

11.) If A is a 3x3 matrix and det(A)=0, then the columns of A are dependent.

12.) For any mxn matrix A, the column space of A is the same as the range.

Please give an explanation as to why each problem is true or false.

7) true

8)true

9)false,,since T(p(x)+p(y))is not eqaul to T(p(x))+T(p(y))

10)true

11)true

12)true

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