Homework Sets HW 15 Sec 4.3 HW 15 Sec 4.3: Problem 1 Problem User Settings Previ
ID: 3115211 • Letter: H
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Homework Sets HW 15 Sec 4.3 HW 15 Sec 4.3: Problem 1 Problem User Settings Previous Problem List Next Grades (1 point) The trace of a square nXn matrix A = (a) is the sum at an ... + aim of the entries on its main diagonal Problems Let V be the vector space of all 2 x 2 matrices with real entries, Let H be the set of all 2 x 2 matrices with real entries that have trace 0, is H a subspace of the vector space V? Problem 1 Problem 2 1. Is H nonempty? H is nonempty 4 Problem 3 Problem 4 Problem 5 2. Is H closed under addition? If it is, enter CLOSED. If It is not, enter two matrices in H whose sum is not in H, using a comma separated list and 1 21 56 syntax such as ((1.2,(3,4) . (15.6.17.811 for the answer [ , 2 . (Hintto show that H is not closed under addition, it is sufficient to find two trace zero matrices A and B such that A +B has nonzero trace) Problem 6 Problem 7 Problem a Problem 9 Problem 10 3. Is H closed under scalar multiplication? If it is, enter CLOSED, If it is not, enter a scalar in R and a matrix in H whose product is not in H, using a Problem 11 Problem 12 comma separated list and syntax such as 2, (3,4,5,6) for the answer 2, IS 6 (Hintto show that H is not closed under scalar multiplication, it is sufficient to find a real number r and a trace zero matrix A such that rA has nonzero trace .) Problem 13 Problem 14 AM Problem 15 Problem 16 AM 4. Is H a subspace of the vector space V? You should be able to justify your answer using the subspace test (Theorem 4.5) and your answers to parts 1-3. His a subspace of v Problem 17 AM Problem 18 Problem 19 Problem 20 Note: In order to get credit for this problem all answers must be correct Problem 21 Problem 22 Preview My Answers submit Answers Problem 23 You have attempted this problem 2 times. Your overall recorded score is 0%.Explanation / Answer
1) ANSWER:
H is not an empty set.Moreover H is a subspace of a vector space V.
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2).Answer.
Yes, H is closed under addition.Moreover no need to find the trace of H.
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3) Answer.
incomplete question
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4).Answer:
incomplete wuestion
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