Recent content by elo

  1. E

    Showing that a linear transformation from P3 to R4 is an isomorphism?

    Okay: since I can get a 4-dimensional x out of T, the image of T must span R4. The starting space P3 has four dimensions. By rank-nullity, the dimension of the kernel of the transformation plus the dimension of its image must equal the dimension of P3; since the dimension of the image is four...
  2. E

    Showing that a linear transformation from P3 to R4 is an isomorphism?

    I have a linear transformation, T, from P3 (polynomials of degree ≤ 3) to R4 (4-dimensional real number space). I have a second linear transformation, U, from R4 back to P3. In the first step of this four-step problem, I have shown that the composition TU from R4 to R4 is the identity linear...