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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 ? 

          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 ?
Show more…
q2let theseth a is set h a vector space justify your answer b is the set h close with respect to scalar multiplication justify your answer q3determine if the set h of all matrices of the for 12718

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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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 ?
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Transcript

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00:01 The dimension of vector space.
00:03 How do you find the dimension of vector space? which is equal to number of elements in basis set.
00:13 Second one, we need to find the answer for basis, which is a set of all elements in a vector space is called a basis...
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