Linear Transformations: please help!
Let V and W be vector spaces. A function L, with domain V and range W us called a linear transformation from V to W iff
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(cm) = 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)