Lin Alg Check points Mod 13-TBD
T/F: Suppose L is lower-triangular and invertible. The system Ly=b may be solved by
forward substitution. - answer True
T/F: Suppose A has a LU-decomp and we want to solve for Ax=bi for many different bi.
Then, first finding the LU-decomp of A may be computationally beneficial - answer True
T/F: Suppose A is an nxn matrix with LU-decomp A=LU. If c element of real numbers,
satisfies Lc=b and Uy=c, then y solves the equation Ax=b - answer True
T/F: Let v be an element of the real numbers. If v dot v=0, then v=0. - answer True
T/F: Let a, b, c be element of real numbers. If a,b are orthogonal and b,c are orthogonal,
then a,c are orthogonal. - answer False. consider non zero a=c
T/F: If S is a non-empty subset of Rn such that any linear combination of vectors in S is
again a vector in S, then S is a subspace of Rn - answer True
T/F: Any line or plane in R3 is a subspace of R3 - answer False
T/F: If S is a non-empty subset of Rn, then span(S) is a subspace of Rn - answer True
T/F: Suppose L is lower-triangular and invertible. The system Ly=b may be solved by
forward substitution. - answer True
T/F: Suppose A has a LU-decomp and we want to solve for Ax=bi for many different bi.
Then, first finding the LU-decomp of A may be computationally beneficial - answer True
T/F: Suppose A is an nxn matrix with LU-decomp A=LU. If c element of real numbers,
satisfies Lc=b and Uy=c, then y solves the equation Ax=b - answer True
T/F: Let v be an element of the real numbers. If v dot v=0, then v=0. - answer True
T/F: Let a, b, c be element of real numbers. If a,b are orthogonal and b,c are orthogonal,
then a,c are orthogonal. - answer False. consider non zero a=c
T/F: If S is a non-empty subset of Rn such that any linear combination of vectors in S is
again a vector in S, then S is a subspace of Rn - answer True
T/F: Any line or plane in R3 is a subspace of R3 - answer False
T/F: If S is a non-empty subset of Rn, then span(S) is a subspace of Rn - answer True
