Q.2. Let the set H be a vector space. Justify your answer. Is the set H closed with respect to scalar multiplication? Justify your answer.
Q.3. Determine if the set H of all matrices of the form 0
is a subspace of M. Here p, q, and r represent arbitrary real numbers.
Q.4. Let H be the set of all vectors of the form shown below. Is H a subspace of *? Justify your answer for each case. Here p, q, r, and s represent arbitrary real numbers.
52p+-s p-3r (a) 5p+3q 0
p-s p-5 (b) p+3q r+3q
1
Q.5. Let A be the matrix 0 1 2.
a) Determine if u is in the null space of A. Could u be in the column space of A? Justify.
b) Determine if v is in the column space of A. Could v be in the null space of A? Justify.
c) Find the spanning sets for the column space of A, the row space of A, and the null space of A.
Q.6. Let A = 0 1 2 4 1 0 1 3 -2.
a) If the column space of A is a subspace of R, what is the value of ?
b) If the null space of A is a subspace of R, what is the value of ?
