Homework Answers
Determine if (n!) converges, and justify your answer. (2n)! n=1
Determine if (n!) converges, and justify your answer. (2n)! n=1
2. Determine whether the following equations are linear in r, y and z: justify your answer.
2. Determine whether the following equations are linear in r, y and z: justify your answer.
Find the standard matrix of T ( Call it A) Is T one-to-one? Justify your answer...
Find the standard matrix of T ( Call it A)
Is T one-to-one? Justify your answer
Is T onto ? Justify your answer
-> Question 5. (20 pts) Let T : R? R? be a linear transformation such that T(:21,22) = (21 - 222, -21 +3.22, 3.11 - 2:02). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations...
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
Do the following series converges or diverges. Justify your answer. (a) sin?(n) n2 n= i M8...
Do the following series converges or diverges. Justify your answer. (a) sin?(n) n2 n= i M8 M8 nh (b) 22n 221 n=1
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3...
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
Determine if the statement is true or false, and justify your answer. If u4 is not...
Determine if the statement is true or false, and justify your answer. If u4 is not a linear combination of {u1, u2, u3}, then {u1, u2, u3, u4} is linearly independent. A) False. Consider u1 = (1, 0, 0), u2 = (0, 1, 0), u3 = (0, 0, 1), u4 = (0, 1, 0). B) False. Consider u1 = (1, 0, 0), u2 = (1, 0, 0), u3 = (1, 0, 0), u4 = (0, 1, 0). C) True. The...
SELECT ONE ANSWER FOR EACH QUESTION. JUSTIFY YOUR ANSWER FOR ANY CREDIT. 1. Which of the...
SELECT ONE ANSWER FOR EACH QUESTION. JUSTIFY YOUR ANSWER FOR ANY CREDIT. 1. Which of the following compounds is aromatic (2 pts each)? A) B) C) D) E) 2. Which of the following compounds is antiaromatic? B) C) D) E) A) Page 7 of 14 Explain why please!!
4. (3 points each-18 points) Which of the following transformations are linear? Justify your answer by...
4. (3 points each-18 points) Which of the following transformations are linear? Justify your answer by proving that it's linear or not linear. The input is u-(v1,v2) є R2 (a) T(u)= (v2,vi) (b) T(u)= (vi, vi) (c) T(t) = (0,v) 0,1 (e) T(v) v-2 (f) T(v) v2
For each of the following functions, determine whether or not they are (i) one-to-one and i) onto. Justify your answers...
For each of the following functions, determine whether or not they are (i) one-to-one and i) onto. Justify your answers (a) f : R-{0} → R and f(x) = 3r-1/x (b) g : R _ {1} → R and g(x) = x + 1/(x-1) (c) l : S → Znon-reg and l(s) = number of 1's in s, for all strings s E S, where s is the set of all strings of O's and 1's. (d) 1 : S...
Determine if (n!) converges, and justify your answer. (2n)! n=1
2. Determine whether the following equations are linear in r, y and z: justify your answer.
Find the standard matrix of T ( Call it A)
Is T one-to-one? Justify your answer
Is T onto ? Justify your answer
-> Question 5. (20 pts) Let T : R? R? be a linear transformation such that T(:21,22) = (21 - 222, -21 +3.22, 3.11 - 2:02). (1). Find the standard matrix of T (call it A). (2). Is T one-to-one? Justify your answer. (3). Is T onto? Justify your answer.
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
Do the following series converges or diverges. Justify your answer. (a) sin?(n) n2 n= i M8 M8 nh (b) 22n 221 n=1
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
SELECT ONE ANSWER FOR EACH QUESTION. JUSTIFY YOUR ANSWER FOR ANY CREDIT. 1. Which of the following compounds is aromatic (2 pts each)? A) B) C) D) E) 2. Which of the following compounds is antiaromatic? B) C) D) E) A) Page 7 of 14 Explain why please!!
4. (3 points each-18 points) Which of the following transformations are linear? Justify your answer by proving that it's linear or not linear. The input is u-(v1,v2) є R2 (a) T(u)= (v2,vi) (b) T(u)= (vi, vi) (c) T(t) = (0,v) 0,1 (e) T(v) v-2 (f) T(v) v2
For each of the following functions, determine whether or not they are (i) one-to-one and i) onto. Justify your answers (a) f : R-{0} → R and f(x) = 3r-1/x (b) g : R _ {1} → R and g(x) = x + 1/(x-1) (c) l : S → Znon-reg and l(s) = number of 1's in s, for all strings s E S, where s is the set of all strings of O's and 1's. (d) 1 : S...
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