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Problem 5: Find the Roll-Pitch-Yaw angle representation of the following rotation matrix. If ther...
Do 3 and 4 please Problem 3: Find the ZYZ Euler angle representation of the following...
Do 3 and 4 please
Problem 3: Find the ZYZ Euler angle representation of the following rotation matrix. If there is infinite number of solutions, you only need to provide one set of solutions. If there are only two sets of solutions, you need to provide both sets. -0.766 0.6428 0 R=10.6248 0.766 0 Problem 4: Find the ZYZ Euler angle representation of the following rotation matrix. If there is infinite number of solutions, you only need to provide one...
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix w...
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
Cousider the matrix A- 456. Which of the sets is not a subepace of R7 1...
Cousider the matrix A- 456. Which of the sets is not a subepace of R7 1 2 3 L7 8 9 (A) The set of all vectors e in R uch that A-o (B) The set of all vectors bin R such that A-b has a solution (C) The set of all vectors a in R such that Aa (D) All of the above sets are subspaces of R3. 6. Let A be a 6 x 6 matrix. Suppose that...
Problem 5. A subset A C R is an affine subspace of R" if there exists a vector bE R" and an under...
Problem 5. A subset A C R is an affine subspace of R" if there exists a vector bE R" and an underlying vector subspace W of R" such that (a) Describe all the affine subspaces of R2 which are not vector subspaces of R2 (b) Consider A E Rnx, bER" and the system of linear equations AT . Prove that: (i) if Ais consistent, then its solution set is an affine subspace of R" with underlying (ii) if At...
Which of the following is/are true? You can find the resultant rector and rerultant angle both...
Which of the following is/are true? You can find the resultant rector and rerultant angle both You can find the resultant vector and A resultant angle both using the component and experimental method You need both the graphical method and B. experimental method to successfully find the resultant vector, only one is insufficient All three methods are important and required to find the resultant vector and resultant angle All of DD above Ein the praphical method
Question 5: Find the exact solutions in the time domain using dsolve. Recall the matrix representation for our two-vess...
Question 5: Find the exact solutions in the time domain using dsolve. Recall the matrix representation for our two-vessel water clock is: d又 -=Ax, where A= DE: Hint: Start with the code below. Then enter A, x0, and the DE. Use dsolve. syms yl (t) y2 (t) Use dot notation to access the components of the solution Question 5: Record your solution for the two unknowns y1(t) and y2(t). The first is given for you y2 (t) = y, (t)...
Problem 5. A subset A C R', is an afǐпє subspace of Rn if there exists a vector b underlying vect...
Problem 5. A subset A C R', is an afǐпє subspace of Rn if there exists a vector b underlying vector subspace W of R" such that Rn and an (a) Describe all the affine subspaces of IR2 which are not vector subspaces of R2 (b) Consider A e R"Xn, beR" and the system of linear equations Ar- b. Prove that: (i) if A-b is consistent, then its solution set is an affine subspace of R" with underlying (ii) if...
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...
There are two bevel gears in mate (a pinion and gear) determine the maximum diametral pitch...
There are two bevel gears in mate (a pinion and gear) determine the maximum diametral pitch (or closest to SF) based on the bending equations and the data below: (hint: use iterative approach, meaning it make take more than one try) (Also recall that diametral pitches are standardized, find the one the closest to standardized value while satisfying the FOS) . Determine the optimal diametral pitch, P, for the pinion (use bending equations) . Design/Safety Factor (SF)2.00 Overall Factor of...
2 Solving the Basic Factors From Problem s in Project 1, you know that if you have a factorizatio...
2 Solving the Basic Factors From Problem s in Project 1, you know that if you have a factorization r-10... o Q2 o @1 in R[D], then (since all the Q, commute with one another), you can find solu- tions to L(y) 0 by solving Qt(y) 0 for i 1,2,...,r. In other words, the IVP has a unique solution. 2.I Factors of Degree One Because of the discussion above, we can see that it will be useful to search out...
Do 3 and 4 please
Problem 3: Find the ZYZ Euler angle representation of the following rotation matrix. If there is infinite number of solutions, you only need to provide one set of solutions. If there are only two sets of solutions, you need to provide both sets. -0.766 0.6428 0 R=10.6248 0.766 0 Problem 4: Find the ZYZ Euler angle representation of the following rotation matrix. If there is infinite number of solutions, you only need to provide one...
Problem: Given a rotation R of R3 about an arbitrary axis through a given angle find the matrix which represents R with respect to standard coordinates. Here are the details: The axis of rotation is the line L, spanned and oriented by the vector v (1,一1,-1) . Now rotate R3 about L through the angle t = 4 π according to the Right 3 Hand Rule Solution strategy: If we choose a right handed ordered ONB B- (a, b,r) for...
Cousider the matrix A- 456. Which of the sets is not a subepace of R7 1 2 3 L7 8 9 (A) The set of all vectors e in R uch that A-o (B) The set of all vectors bin R such that A-b has a solution (C) The set of all vectors a in R such that Aa (D) All of the above sets are subspaces of R3. 6. Let A be a 6 x 6 matrix. Suppose that...
Problem 5. A subset A C R is an affine subspace of R" if there exists a vector bE R" and an underlying vector subspace W of R" such that (a) Describe all the affine subspaces of R2 which are not vector subspaces of R2 (b) Consider A E Rnx, bER" and the system of linear equations AT . Prove that: (i) if Ais consistent, then its solution set is an affine subspace of R" with underlying (ii) if At...
Which of the following is/are true? You can find the resultant rector and rerultant angle both You can find the resultant vector and A resultant angle both using the component and experimental method You need both the graphical method and B. experimental method to successfully find the resultant vector, only one is insufficient All three methods are important and required to find the resultant vector and resultant angle All of DD above Ein the praphical method
Question 5: Find the exact solutions in the time domain using dsolve. Recall the matrix representation for our two-vessel water clock is: d又 -=Ax, where A= DE: Hint: Start with the code below. Then enter A, x0, and the DE. Use dsolve. syms yl (t) y2 (t) Use dot notation to access the components of the solution Question 5: Record your solution for the two unknowns y1(t) and y2(t). The first is given for you y2 (t) = y, (t)...
Problem 5. A subset A C R', is an afǐпє subspace of Rn if there exists a vector b underlying vector subspace W of R" such that Rn and an (a) Describe all the affine subspaces of IR2 which are not vector subspaces of R2 (b) Consider A e R"Xn, beR" and the system of linear equations Ar- b. Prove that: (i) if A-b is consistent, then its solution set is an affine subspace of R" with underlying (ii) if...
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...
There are two bevel gears in mate (a pinion and gear) determine the maximum diametral pitch (or closest to SF) based on the bending equations and the data below: (hint: use iterative approach, meaning it make take more than one try) (Also recall that diametral pitches are standardized, find the one the closest to standardized value while satisfying the FOS) . Determine the optimal diametral pitch, P, for the pinion (use bending equations) . Design/Safety Factor (SF)2.00 Overall Factor of...
2 Solving the Basic Factors From Problem s in Project 1, you know that if you have a factorization r-10... o Q2 o @1 in R[D], then (since all the Q, commute with one another), you can find solu- tions to L(y) 0 by solving Qt(y) 0 for i 1,2,...,r. In other words, the IVP has a unique solution. 2.I Factors of Degree One Because of the discussion above, we can see that it will be useful to search out...
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