2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [ 3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2) and (5, −1, 4) respectively.
(i) Show that P Q~ = 2i − j + k.
(ii) Show that P R~ = 3i − 3j + 3k.
(iii) Calculate the vector product P Q~ × P R~ .
(iv) Calculate the scalar product P Q~ · P R~ .
(v) Use your answer to (iv) to calculate the angle between the vectors P Q~ and P R~ , giving your answer to the nearest degree.
![2. (a) Consider the following matrices: 18 -6 co en B C = 17 1] [3 -3 [ 5 2 3 -4 -1] 2 -3 (i) Calculate A+ B, (ii) Calculate](http://img.homeworklib.com/questions/c72a2340-45d6-11ec-a8e7-bbe1676b9551.png?x-oss-process=image/resize,w_560)
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dr - 0 dz 1 dx P x² + y² + 하공 8. OP 11 위공...
dr - 0 dz 1 dx P x² + y² + 하공 8. OP 11 위공 d츠 1 ㅇ d² 0= 이 1) Here are two rank 1 tensors of differing types, written in Cartesian co-ordinates: 1 -4 vi(x, y, z) = wi(x,y,z) 2 3 a) Calculate their scalar product viw. (2 marks) b) Using the appropriate tensor transform equations, and expressions for the partial derivatives obtained from class, transform both tensors into cylindrical polar co-ordinates (r, 0, z). (6...
Parts d and e needed! 1) Here are two rank 1 tensors of differing types, written...
Parts d and e needed!
1) Here are two rank 1 tensors of differing types, written in Cartesian co-ordinates: 1 -4 vi(x, y, z) = wi(x,y,z) 2 3 a) Calculate their scalar product viw. (2 marks) b) Using the appropriate tensor transform equations, and expressions for the partial derivatives obtained from class, transform both tensors into cylindrical polar co-ordinates (r, 0, z). (6 marks) c) Calculate the scalar product of the transformed tensors, and show that the answer is the...
with clear writing please QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3...
with clear writing please
QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3 i+ 3j +3k find: (a) the magnitude of B A B Ax B ii. iIl (b) If i, j, k are the unit vectors of the x, y, and z axes, evaluate: jx k iV. ix i
6 ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is...
6
ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
can anyone check my answers? thx! 1. In all parts of Problem 1 (this page and...
can anyone check my answers? thx!
1. In all parts of Problem 1 (this page and next), let RQ R denote the points: (a) (4 points) Find the vectors PQ from P to Q and PR from P to R. Pa= [ ] PR - [ ] (b) (4 points) Find a parametrization of the line passing through P and Q. P = Porto Wt)= 1-1 yet): - 1+3 21+) = 2+t =<1-,-1+31, 2+t> (0) (4 points) Is R on...
7. Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b)...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a unit vector...
Consider the Markov chains given by the following transition matrices. (1) Q = (1/2 1/2) (we=...
Consider the Markov chains given by the following transition matrices. (1) Q = (1/2 1/2) (we= (1/2 162) (ii) Q = (1 o). /1/3 0 2/3 (1/2 1/2 0 (iv) Q = 1 0 1 0 1 (v) Q = 1 0 1/2 1/2 lo 1/5 4/5) \1/3 1/3 1/3) For each of the Markov chains above: A. Draw the transition diagram. B. Determine whether the chain is reducible or irreducible. Justify your answer. C. Determine whether the chain is...
3. The following matrices are inverses. 11 3 37 1 4 3 A= A-!= 17 -1...
3. The following matrices are inverses. 11 3 37 1 4 3 A= A-!= 17 -1 (-1 -3 1 0 -37 0 1 1 3 4 Solve following system of equations I + + + 3y 4y 3y + + + 32 3 4 = = = b b b 1 (a) when by = 0, b2 = 0, and bg = 0. The solution is z, y, z) = (i) (1,-1,1) (ii) (-1,2,1) (iii) (0,0,0) (iv) (7, -2,0) (b)...
6. 2D vectors Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a)...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a...
1. Find the determinant of the follow ing matrices 1 8 [2 1 B=3 8 10...
1. Find the determinant of the follow ing matrices 1 8 [2 1 B=3 8 10 det BT
dr - 0 dz 1 dx P x² + y² + 하공 8. OP 11 위공 d츠 1 ㅇ d² 0= 이 1) Here are two rank 1 tensors of differing types, written in Cartesian co-ordinates: 1 -4 vi(x, y, z) = wi(x,y,z) 2 3 a) Calculate their scalar product viw. (2 marks) b) Using the appropriate tensor transform equations, and expressions for the partial derivatives obtained from class, transform both tensors into cylindrical polar co-ordinates (r, 0, z). (6...
Parts d and e needed!
1) Here are two rank 1 tensors of differing types, written in Cartesian co-ordinates: 1 -4 vi(x, y, z) = wi(x,y,z) 2 3 a) Calculate their scalar product viw. (2 marks) b) Using the appropriate tensor transform equations, and expressions for the partial derivatives obtained from class, transform both tensors into cylindrical polar co-ordinates (r, 0, z). (6 marks) c) Calculate the scalar product of the transformed tensors, and show that the answer is the...
with clear writing please
QUESTION 1 (Total 15 marks) VECTORS If A -2i+2k and B -3 i+ 3j +3k find: (a) the magnitude of B A B Ax B ii. iIl (b) If i, j, k are the unit vectors of the x, y, and z axes, evaluate: jx k iV. ix i
6
ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
can anyone check my answers? thx!
1. In all parts of Problem 1 (this page and next), let RQ R denote the points: (a) (4 points) Find the vectors PQ from P to Q and PR from P to R. Pa= [ ] PR - [ ] (b) (4 points) Find a parametrization of the line passing through P and Q. P = Porto Wt)= 1-1 yet): - 1+3 21+) = 2+t =<1-,-1+31, 2+t> (0) (4 points) Is R on...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a unit vector...
Consider the Markov chains given by the following transition matrices. (1) Q = (1/2 1/2) (we= (1/2 162) (ii) Q = (1 o). /1/3 0 2/3 (1/2 1/2 0 (iv) Q = 1 0 1 0 1 (v) Q = 1 0 1/2 1/2 lo 1/5 4/5) \1/3 1/3 1/3) For each of the Markov chains above: A. Draw the transition diagram. B. Determine whether the chain is reducible or irreducible. Justify your answer. C. Determine whether the chain is...
3. The following matrices are inverses. 11 3 37 1 4 3 A= A-!= 17 -1 (-1 -3 1 0 -37 0 1 1 3 4 Solve following system of equations I + + + 3y 4y 3y + + + 32 3 4 = = = b b b 1 (a) when by = 0, b2 = 0, and bg = 0. The solution is z, y, z) = (i) (1,-1,1) (ii) (-1,2,1) (iii) (0,0,0) (iv) (7, -2,0) (b)...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? &Define a unit vector. Give an example of a...
1. Find the determinant of the follow ing matrices 1 8 [2 1 B=3 8 10 det BT
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