Math 240 Quiz 2 Questions and Answers 100% Pass

Math 240 Quiz 2 Questions and Answers 100% Pass Properties of subspace of Rn - 0 vecter is in H, if u and v are in H, u + v is in h, if u is in h -> lambda*u is in H Col(A) (column space) - the set of all linear combos of the columns of A Nul(A) (null space) - the set of all solutions to Ax=0 Nul(A) is a subspace of Rn - true Basis for a subspace H - a linearly independent set in H that spans H (the vectors in the set of all solutions) Dim(A) (dimension of subspace) - the number of vectors in the basis for the subspace Rank(A) - dimCol(A) -> the number of lin. indep columns in Col(A) maximum possible rank - the smaller of M and N 2100% Pass Guarantee Katelyn Whitman All Rights Reserved © 2025 rank theorem - If A has n columns: rank(A)+dimNul(A)=n and dimNul(A)+dimCol(A)=n, and rank is the min{m,n} equivalent statements - 1.A is invertible 2. Col(A)=Rn Col(A)=n 4.Rk(A)=n 5.Nul(A)={0} Nul(A)=0 if V1...Vp are in Rn, then Span {V1...Vp} is the same as the column space of the matrix [V1 Vp] - true the set of all solutions of a system of m homogeneous equations in n unknowns is a subspace of Rm - false the columns of an invertible nxn matrix form a basis for Rn - true row operations do not affect linear dependence relations among the columns of a matrix - true a subset H of Rn is a subspace if the zero vector is in H - false, there are more conditions than that 3100% Pass Guarantee Katelyn Whitman All Rights Reserved © 2025 if B is an echelon form of a matrix A, then the pivot columns of B form a basis for ColA - false, pivot columns of A form the basis given vectors v1....vp in Rn, the set of all linear combinations of these vectors is a subspace of Rn - true let H be a subspace of Rn. If x is in H, and y is in Rn, then x+y is in H - false the column space of a matrix A is the set of solutions of Ax=b - false If B={V1...Vp} is a basis for a subspace H and if x=C1V1+...+CpVp, then C1...Cp are the coordinates of x relative to the basis B - true