Let T : V → W be a linear transformation from vector space V to vector space W, both of which are finite-dimensional. Let H be a nonzero subspace of V , and let T(H) = {T(x)| x ∈ H} (i. e., T(H) is the set of images of the vectors in V ). Prove that T(H) is a subspace of W. Also show that dim(T(H)) ≤ dim(H). Recall that dim(H) denotes the dimension of the vector space H.

Lassify the function as linear or quadratic and identify the quadratic, linear, and constant terms. f(x) = (3x + 2)(−6x − 3) linear function; linear term: −21x; constant term: −6 linear function; linear term: −18x2; constant term: −6 quadratic function; quadratic term: 6x2; linear term: 24x; constant term: −6 quadratic function; quadratic term: −18x2; linear term: −21x; constant term: −6

Graph the equation by plotting point x=2

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12