Let A = A basis for the image of A is 9 -6 6 9 Find a basis for the image of A (or, equivalently, for the linear transformation T(x) = Ax). -12 -10] -3 3 -3 3 -12 -10 .

defined by Let Let ƒ : R² → R² be the linear transformation [f] B = B C f(x) = = = 3 2 -2 - -3 x. be two different bases for R². Find the matrix [f] for f relative to the basis B in the domain and C in the codomain. {(-1,2), (3,-7)}, {{-1, -2), (3, 7)},

A linear transformation T : R³ → R² whose matrix is -2 -6 -6 -2 -6 -10 + k| is onto if and only if k +