Ryan Ren Math4A-02-S17-Williams WeBWorK assignment number Week6 is due : 05/15/2017 at 06:01am PDT. The Gauchospace link for the course contains the syllabus, grading policy and other information. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA's or your professor for help. Don't spend a lot of time guessing - it's not very efficient or effective. Give 4 or 5 significant digits for (floating point) numerical answers. For most problems when entering numerical answers, you can if you wish enter elementary expressions such as 2 3 instead of 8, sin(3 pi/2)instead of -1, e (ln(2)) instead of 2, (2 + tan(3)) (4 sin(5)) 6 7/8 instead of 27620.3413, etc. Here's the list of the functions which WeBWorK understands. You can use the Feedback button on each problem page to send e-mail to the professors. If not, which condition(s) below does it fail? (Check all that apply) 1. (1 pt) Does the following set of vectors constitute a vector space? Assume \"standard\" definitions of the operations. The set of vectors in the first quadrant of the plane. A. Yes B. No If not, which condition(s) below does it fail? (Check all that apply) A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication C. There must be a zero vector D. Every vector must have an additive inverse E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property I. Scalar multiplication must be associative J. None of the above, it is a vector space A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication C. There must be a zero vector D. Every vector must have an additive inverse E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property I. Scalar multiplication must be associative J. None of the above, it is a vector space !Answer(s) submitted: (incorrect) 3. (1 pt) Does the following set of vectors constitute a vector space? Assume \"standard\" definitions of the operations. The set of all 2 2 matrices with determinant equal to zero. !Answer(s) submitted: A. Yes B. No If not, which condition(s) below does it fail? (Check all that apply) (incorrect) 2. (1 pt) Does the following set of vectors constitute a vector space? Assume \"standard\" definitions of the operations. The set of all diagonal 2 2 matrices. A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication C. There must be a zero vector D. Every vector must have an additive inverse A. Yes B. No 1 E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property I. Scalar multiplication must be associative J. None of the above, it is a vector space If not, why not? (Check all that apply) A. W is not closed under multiplication by a nonzero scalar B. Not applicable: W is a subspace C. W is not closed under addition D. W does not contain a zero vector !!- Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 6. (1 pt) V=R3 W=(x1 , x2 , x3 )|x3 = 0 Is the given subset W of the vector space V a subspace of V? A. Yes B. No If not, why not? (Check all that apply) 4. (1 pt) Does the following set of vectors constitute a vector space? Assume \"standard\" definitions of the operations. The set of all invertible 2 2 matrices. A. Yes B. No A. W does not contain a zero vector B. W is not closed under addition C. W is not closed under multiplication by a nonzero scalar D. Not applicable: W is a subspace If not, which condition(s) below does it fail? (Check all that apply) A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication C. There must be a zero vector D. Every vector must have an additive inverse E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property I. Scalar multiplication must be associative !Answer(s) submitted: (incorrect) 7. (1 pt) V=R3 S={(1, 0, 0), (0, 1, 0), (3, 5, 2)} Do the vectors in the set S span the vector space V? A. Yes B. No !- !Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 5. (1 pt) V=R2 W={(x, y)|x2 + y2 = 1} Is the given subset W of the vector space V a subspace of V? 8. (1 pt) V=R3 S={(2, 0, 9), (8, 0, 5), (5, 0, 7), (3, 0, 2)} Do the vectors in the set S span the vector space V? A. Yes B. No A. Yes B. No 2 !13.(1 pt) Find the determinant of the matrix 4 5 3 6 8 M= 0 0 0 5 . det (M) = Answer(s) submitted: (incorrect) 9. (1 pt) Finding Kernels Find the kernel of the following transformation. Use a, b, c, and d in your answer. T : P2 P2 , T (at 2 + bt + c) = 2at + b t2 + t + Answer(s) submitted: (incorrect) 14. (1 pt) If the determinant of a 55 matrix A is det (A) = 2, and the matrix B is obtained from A by multiplying the third row . by 9, then det (B) = Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 10. (1 pt) Finding Kernels Find the kernel of the following transformation. Use a, b, c, and d in your answer. T : P2 P2 , T (at 2 + bt + c) = 0 t3 + t2 + t + !- 15. (1 pt) If a det b c 1 1 1 d e = 5 f and 1 d 2 e = 2 3 f a 9 d then det b 9 e = c 9 f a 2 d and det b 3 e = c 4 f a det b c Answer(s) submitted: (incorrect) Answer(s) submitted: 11.(1 pt) Find the determinant of the matrix 2 2 2 0 3 1 0 2 C= 3 2 2 1 0 3 3 2 det (C) = . (incorrect) 16. (1 pt) If a 4 4 matrix A with rows v1 , v2 , v3 , and v4 has determinant det A = 7, v1 7v2 + 4v4 = then det . v3 7v2 + 4v4 Answer(s) submitted: (incorrect) 12. (1 pt) If A and B are 4 4 matrices, det (A) = 1, det (B) = 5, then , det (AB) = det (3A) = , det (AT ) = , det (B1 ) = , det (B4 ) = . Answer(s) submitted: (incorrect) 17. (1 pt) Find the area of the parallelogram defined by the vectors \u0014 \u0015 \u0014 \u0015 9 -5 and . 3 5 Area = . Answer(s) submitted: Answer(s) submitted: (incorrect) (incorrect) 3 Answer(s) submitted: 18. (1 pt) Find the volume of the parallelepiped defined by the vectors 5 -3 -3 4 , 2 , and 5 . 0 -1 -2 . Volume = (incorrect) c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 4 (1 pt) Does the following set of vectors constitute a vector space? Assume "standar " denitions of the operations. The set of all invertible 2 x 2| matrices. Q A. Yes (9:. B. No If not, which condition(s) below does it fail? (Check all that apply) A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication c. There must be a zero vector D. Every vector must have an additive inverse E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property I. Scalar multiplication must be associative CJCJCJCJDDQC] (1 pt) Finding Kernels Find the kernel of the following transformation. Use a, b, o, and d in your answer. T : \\boldP2 } \\bolsz,' T{at2 + bi. + o) 2 0| t3l + til + it + t | ' Online Math Lab resources for this problem: - Linear Transformations - Bases Note: You can eam partiai credit on this probiem. (1 pt) Does the following set of vectors constitute a vector space? Assume "standar " denitions of the operations. The set of all invertible 2 x 2| matrices. Q A. Yes (9:. B. No If not, which condition(s) below does it fail? (Check all that apply) A. Vector spaces must be closed under addition B. Vector spaces must be closed under scalar multiplication c. There must be a zero vector D. Every vector must have an additive inverse E. Addition must be associative F. Addition must be commutative G. Scalar multiplication by 1 is the identity operation H. The distributive property I. Scalar multiplication must be associative CJCJCJCJDDQC] (1 pt) Finding Kernels Find the kernel of the following transformation. Use a, b, o, and d in your answer. T : \\boldP2 } \\bolsz,' T{at2 + bi. + o) 2 0| t3l + til + it + t | ' Online Math Lab resources for this problem: - Linear Transformations - Bases Note: You can eam partiai credit on this probiem