Solve the whim. Ill} Determine which of the following statements is false. A: The dimension of the vector space P7 of polynomials is ti. B: Any line in s3 is a one-dimensional subspace of 13. C: If a vector spaoe V has a basis B = {[11, ......, by} then any set in V containing 3 vectors must be linearlyr dependent. 11] Determine which of the following statements is true. A: If V is a 4-dimensional vector space, then any set of exactly? 4 elements in V is automatically a basis for if. E: If there exists a set {vL ......, v5}1at spans V, then dim V = 5. C: If H is a subspaoe of a Finite-dimensional vector spaoe V, then dim H s dim if. Assume that the malrix A is raw equivalent to E. Find a basis for the row space of the matrix A. 1 3 -4 l} 1 1 3 -4 {II 1 12:14\": 2 4 5 2 4:5: IIII 2 3 2 1 -5 -3 2 l} Ill -3 -11 25 -3 -1 ti 3 ..q. E! [I [I [II II] Solve the problem. 13} If the null spate of a 5 s F matrix is 3-dimensionaL End Rank A, Dim Row A, and Dim Col A. 111] If A is a 5 s 9 matrix, what is the smallest possible dimension of No] A? 15} Find the coordinate vector [x13 of the vector in; relative to the given basis B. .' 3:4[1 +x+xz,l+3x+212,4+x2}and J:=-2+4.t+2xi