vectors denoted by bold

i) for every

**m**and

**n**in V, L(

**m**+

**n**)=L(

**m**) + L(

**n**)

ii) for every

**m**in V and every scalar c, L(c

**m**) = c(L(

**m**))

In each of the following problems, determine whether or not the function L is really a linear transformation. You are to use i and ii to determine this.

a) V is the vector space of real numbers, as is W. L(x) = 3x-2, where r is a real number

b)V is the vector space of ordered pairs of real numbers. W is the vector space of real numbers. L ( (x,y ) ) = ax+by where a and b are

__fixed__real numbers

c) V is the vector space of 2X2 matrices with real entries and W is the vector space of real numbers.

where L(matrix) = determinant of the matrix (i could not draw the matrix on this form)