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is on diagonal kl-n,... ,n-1. If w- Av, what is the derivative ôwi/8a r, suppose wi = max (v2i-1,V2i). Find all awi/avi 8 In a max-pooling laye 9 To underetand sthe ehai is on diagonal kl-n,...
(1 point) Suppose 11-8 12 -9 A: Find an invertible matrix P and a diagonal matrix...
(1 point) Suppose 11-8 12 -9 A: Find an invertible matrix P and a diagonal matrix D so that A PDP1.Use your answer to find an expression for A7 in terms of P, a power of D, and P-1 in that order.
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38]...
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38] 2. For this problem, use matrices A = La ), B=1 _Jandc=lo 9]. Suppose that the matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A. 3. Find a number a so that the vectors v = [3 2 a) and w = [2a -1 3] are orthogonal (perpendicular). 4. For the vector...
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero...
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero orthogonal vectors. Explain why WR Two subspaces are the same when one subspace is a subset of the other subspace. Two subspaces are the same when they are spanned by the same vectors Two subspaces are the same when they are subsets of the same space Two subspaces are the same when they have the same dimension Incorrect 0/1 pts Question 10 Let U...
Problem 1. (total: 20 points) Find (r) for all nine (9) of the degenerate n =...
Problem 1. (total: 20 points) Find (r) for all nine (9) of the degenerate n = 3 states of a hydrogen atom. Here show the radial wave functions for hydrogen, R3(r), where I = 0,1,2. R3o = 31aa-82 (1-** 2: 0°)exp(-r/3a) Rs1 20 6 2 /(1-19) exp(-1/3a) B92 - pitza 22 (?exp=r730)
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1,...
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1, 0 < arctan(x) < x2 Give the best possible bound. And so 0 < an arctan(n) = <bn n/(2n^6) Since 0 < an <bn, which of the following test should we apply? A. The integral test B. The comparison test. C. The nth term test for divergence D. The ratio test E. The limit comparison test F. The p-series test G. The root test...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine all such triangles. b. Find the smallest two such tri...
8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine all such triangles. b. Find the smallest two such triangles.
8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine...
Let Y_1~Gamma(α=3,β=3), Y_2~Gamma(α=5,β=1), and W=2Y_1+6Y_2. a) (9 pts) Find the moment generating function ofW Justify all...
Let Y_1~Gamma(α=3,β=3), Y_2~Gamma(α=5,β=1), and W=2Y_1+6Y_2.
a) (9 pts) Find the moment generating function ofW Justify all steps b) (3 pts) Based on your result in part (a), what is the distribution of W(name and parameters)? n 2N(O, I) 2. IfZ NO, 1), then Ux(1) 3. ItY Gmmaa,B) and W then Wx(n) - s, and i-1 7. y's~ Poisson(W (i-l, ,Rind) and U-ŽYi, then U-Poisson(XA) 8 If%-Gamma(a, β) (i-I, ,Rind) and U-ΣΥί , then U~Gamma( ,4 β).(Note: all same β) 9...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all inte...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
Problem 8. 1 point) Suppose that f(x) (9 6x)e Note: Several parts of this problem r (A) List all ...
question 8 has parts (A-I)
Problem 8. 1 point) Suppose that f(x) (9 6x)e Note: Several parts of this problem r (A) List all the critical values of fx) Note: If there are no critical values, enter NONE require answers entered in interval notation. Note, with interval notation, you can enter the empty set as (B) Use interval notation to indicate where f(z) is increasing increasing (C) Use interval notation to indicate where f(z) is decreasing Decreasing (D) List the...
(1 point) Suppose 11-8 12 -9 A: Find an invertible matrix P and a diagonal matrix D so that A PDP1.Use your answer to find an expression for A7 in terms of P, a power of D, and P-1 in that order.
1. Find a 2x2 matrix A if for the vector v= [R], Av = [4 +38] 2. For this problem, use matrices A = La ), B=1 _Jandc=lo 9]. Suppose that the matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A. 3. Find a number a so that the vectors v = [3 2 a) and w = [2a -1 3] are orthogonal (perpendicular). 4. For the vector...
0/1 pts Inooreat Question 9 Suppose W is a subspace of R" spanned by n nonzero orthogonal vectors. Explain why WR Two subspaces are the same when one subspace is a subset of the other subspace. Two subspaces are the same when they are spanned by the same vectors Two subspaces are the same when they are subsets of the same space Two subspaces are the same when they have the same dimension Incorrect 0/1 pts Question 10 Let U...
Problem 1. (total: 20 points) Find (r) for all nine (9) of the degenerate n = 3 states of a hydrogen atom. Here show the radial wave functions for hydrogen, R3(r), where I = 0,1,2. R3o = 31aa-82 (1-** 2: 0°)exp(-r/3a) Rs1 20 6 2 /(1-19) exp(-1/3a) B92 - pitza 22 (?exp=r730)
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1, 0 < arctan(x) < x2 Give the best possible bound. And so 0 < an arctan(n) = <bn n/(2n^6) Since 0 < an <bn, which of the following test should we apply? A. The integral test B. The comparison test. C. The nth term test for divergence D. The ratio test E. The limit comparison test F. The p-series test G. The root test...
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine all such triangles. b. Find the smallest two such triangles.
8. 2mn, b-m2-n, and c = m2 + n2 be the sides of a a. Let a Pythagorean triangle. Suppose that b -a + 1. Show that (m - n)2 - 2n2 1, and determine...
Let Y_1~Gamma(α=3,β=3), Y_2~Gamma(α=5,β=1), and W=2Y_1+6Y_2.
a) (9 pts) Find the moment generating function ofW Justify all steps b) (3 pts) Based on your result in part (a), what is the distribution of W(name and parameters)? n 2N(O, I) 2. IfZ NO, 1), then Ux(1) 3. ItY Gmmaa,B) and W then Wx(n) - s, and i-1 7. y's~ Poisson(W (i-l, ,Rind) and U-ŽYi, then U-Poisson(XA) 8 If%-Gamma(a, β) (i-I, ,Rind) and U-ΣΥί , then U~Gamma( ,4 β).(Note: all same β) 9...
In questions 1-8, find the limit of the sequence. sin n cos n 2. 37 /n sin n 3. 4. cos rn 5. /n sin n o cos n n! 9. If c is a positive real number and lan) is a sequence such that for all integer n > 0, prove that limn →00 (an)/n-0. 10. If a > 0, prove that limn+ (sin n)/n 0 Theorem 6.9 Suppose that the sequence lan) is monotonic. Then ta, only if...
question 8 has parts (A-I)
Problem 8. 1 point) Suppose that f(x) (9 6x)e Note: Several parts of this problem r (A) List all the critical values of fx) Note: If there are no critical values, enter NONE require answers entered in interval notation. Note, with interval notation, you can enter the empty set as (B) Use interval notation to indicate where f(z) is increasing increasing (C) Use interval notation to indicate where f(z) is decreasing Decreasing (D) List the...
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