Linear Algebra

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Section 3.2 Subspaces: Problem 1 (1 point) ATTEMPT NOT ACCEPTED - Please submit answers again (or request new version if necessary). Determine which of the following subsets of IR * are subspaces of IR3x3 2 1. The 3 x 3 matrices with all zeros in the second row ? 2. The upper triangular 3 x 3 matrices 2 3. The 3 x 3 matrices in reduced row-echelon form v 4. The invertible 3 x 3 matrices ? 5. The singular 3 x 3 matrices 6. The symmetric 3 x 3 matrices 2 7. The 3 x 3 matrices whose entries are all integers 2 v 8. The 3 x 3 matrices with trace O (the trace of a matrix is the sum of its diagonal entries) Yes No er to get credit for this problem all answers must be correct. Preview My Answers Submit AnswersSection 3.2 Subspaces: Problem 10 (1 point) 1 5 Let A = 1 2 4 V Is v in N(A)? Type "yes" or "no". Is w in N(A)? Type "yes" or "no" Is x in N(A)? Type "yes" or "no".Section 3.2 Subspaces: Problem 11 (1 point) Show that the vectors (1, 2, 1), (1, 3, 1), (1, 4, 1) do not span Is by giving a vector not in their span: NOTE: Enter the vector using angle brackets (use the "less than " symbols.)Section 3.2 Subspaces: Problem 12 (1 point) Let A 1 2 -2 -4 6 Find a spanning set for the null space of A. N(A) = spanSection 3.2 Subspaces: Problem 13 (1 point) Let 6 12 4 3 3 A = 6 12 -7 15 6 Find a spanning set for the null space of A. N(A) = spanSection 3.2 Subspaces: Problem 2 (1 point) Determine which of the following subsets of , are subspaces of P4. V 1. S is the subset consisting of those polynomials of the form p() = 1* + c. 2. S is the subset consisting of those polynomials satisfying p(5) = 0. ? V 3. S is the subset consisting of those polynomials of degree exactly three 4. S is the subset consisting of those polynomials of the form p(x) = ar + br. ? 5. S is the subset consisting of those polynomials satisfying p(5) > 0 2 Yes N No er to get credit for this problem all answers must be correct. Preview My Answers Submit AnswersSection 3.2 Subspaces: Problem 3 (1 point) Determine which of the following subsets of IRs are subspaces of IR" ? v 1. {[3r, -5x, 4x] | x arbitrary number } ? v 2. { [I, y, =[ | 5x - 4y + 72 = -3} v 3. { [r, y, = (x2 0, 720, 220) ? v 4. {[z, y, =[ | - 6 + 8y = 0, 97 + 32 = 0} v 5. { [r, 1 + 6, 1 - 8)"|x arbitrary number } 2 v 6. { 3x - 7y, -5x + 2y, 4x - 2y|" | I, 1/ arbitrary numbers } 7. { [r, y, =|61 - By -92 = 0} Yes N No er to get credit for this problem all answers must be correct. Preview My Answers Submit AnswersSection 3.2 Subspaces: Problem 4 (1 point) Let W be the subset of R* consisting of all vectors such that $1 -212 = 41; and 201 = Is + 314. Determine if W is a subspace of IR" and check the correct answer(s) below. A. W is not a subspace because it does not have a zero element. B. W is a subspace because it can be written as N(A) for some matrix A. C. W is a subpace because it has a zero element. OD. W is not subspace because it does not have additive closure. Preview My Answers Submit AnswersSection 3.2 Subspaces: Problem 5 (1 point) Let W be the subset of R" consisting of all vectors such that =1 + 2 + ", > 2. Determine if W is a subspace of IR" and check the correct answer(s) below. A. W is a subspace because it can be written as N(A) for some matrix A. OB. W is not a subspace because it does not contain the zero vector. OC. W is a subspace because it can be expressed as W = span {v1, ..., Vn} OD. W is not a subspace because it is not closed under scalar multiplication. Preview My Answers Submit AnswersSection 3.2 Subspaces: Problem 6 (1 point) b - 2d 5b + d Let W be the set of all vectors where b and d are real. b + 3d d Determine if W is a vector space and check the correct answer below. A. W is a vector space because it can be expressed as W = span ( V1, ..., Vn} B. W is not a vector space because it does not have a zero element. OC. W is a vector space because it contains the zero element. D. W is not a vector space because it does not have additive closure.Section 3.2 Subspaces: Problem 7 (1 point) 4 -5 6 Express the vector v = as a linear combination of X = and y = -5 -5 15 Note: You can earn partial credit on this problem. Preview My Answers Submit AnswersSection 3.2 Subspaces: Problem 8 (1 point) -1 6 15 Let v1 = 4 -1 , and y = -2 h For what value of h is y in the plane spanned by vi and v2? h =Section 3.2 Subspaces: Problem 9 (1 point) 30 - 26 Let W be the set of all vectors of the form Find vectors at and 1 in R such that W = span {{, p} h 1 = 1 =