Homework Answers
Rotation Matrix can be given as ...
a. Here theta in this case, Angle between Jx and Ix is 270 degree.
b. Here theta in this case, Angle between Jx and Ix is 180 degree.
c. Here theta in this case, Angle between Jx and Ix is θ degree.
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3. Obtain the rotation matrix, which converts base J's coordinates into base I's coordinates (RJ)...
In the 3D Cartesian system the rotation matrix is around the z-axis is (a 2D rotation):...
In the 3D Cartesian system the rotation matrix is around the
z-axis is (a 2D rotation):
Where
is the angle to rotate. Then rotation from A to A' is can be
represented via matrix multiplications: [A'] = [R][A]
Such a rotation is useful to return a system solved in
simplified co-ordinates to it's original co-ordinate system,
returning to original meaning to the answer. A full 3D rotation is
simply a series of 2D rotations (with the appropriate matrices)
Question: If...
3 (b) Write the following systems of linear equations as matrix equation and then as an...
3 (b) Write the following systems of linear equations as matrix
equation and then as an augmented matrix:
(4marks)
(d) Use Cramer’s rule to solve the system of 2 linear equations
in 3(b). (7marks)
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1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint...
1. Let be the operator on whose matrix with respect to the standard basis is . a) Verify the result of proof " is normal if and only if for all " for question 1. Note: stands for adjoint b) Verify the result of proof "Orthogonal eigenvectors for normal operators" for question 1. The proof states suppose is normal then eigenvectors of corresponding to distinct eigenvalues are orthogonal. We were unable to transcribe this imageWe were unable to transcribe this...
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...
Problem: Find the matrix which represents in standard coordinates the transformation S : R2 → R2...
Problem: Find the matrix which represents in standard coordinates the transformation S : R2 → R2 which shear parallel to the line L ai , where a (3,6) such that a gets transformed into a s, with s (-18,9) Solution The approach we take demonstrates how much convenience can be gained by being able to work with respect to coordinates which are specially adapted to the situation at hand. We compute the matrix S in two steps 1. We find...
Which of the following is the solution to the differential equation with the initial condition y(1)...
Which of the following is the solution to the differential
equation
with the initial condition y(1) = -1/2
A.
B.
C.
D.
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The system results from an approximation to the Hodgkin-Huxley equations, which model the transm...
The system results from an approximation to the Hodgkin-Huxley equations, which model the transmission of neural impulses along an axon. (a) Determine all critical points of the given system of equations. [Write your points in ascending order of their x-coordinates.] (___, ___) (___, ___) (___, ___) (b) Classify the critical points by investigating the approximate linear system near each one. **Choose one of the 3 in the () to fill in the blank** The critical point is _______(a saddle, a...
Which of the following is the residual plot for the data in the given table? x ...
Which of the following is the residual plot for the data in the
given table?
x
1
2
3
4
5
6
y
15
19
18
31
18
31
a)
b)
c)
d)
e) None of the above
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
In the figure (Figure 1), the following EN and XY coordinates for points A through C...
In the figure (Figure 1), the following EN and XY coordinates for points A through C are given. Determine a 2-D conformal coordinate transformation, to convert the XY coordinates into the EN system. State Plane Coordinates (m) Arbitrary Coordinates (m) Point A 651779.323 290831.221 5804.32 3573.76 B 651369.152 290542.892 3543.59 2773.42 3857.64 3749.59 Figure 〈 1011 〉 Eg-EA アTA Part A What is the scale factor? Express your answer to six significant figures. View Available Hint(s) 8- Submit Part B...
Please answer today! I will upvote/rate. Best fitting line. Matrix. 5. Predicting Populatioin The data below records the population of Irvine, CA (in thousands of people) for the years 2010-...
Please answer today! I will upvote/rate.
Best fitting line. Matrix.
5. Predicting Populatioin The data below records the population of Irvine, CA (in thousands of people) for the years 2010-2016: Year Population 220 2010 229 2011 2012 236 2013 247 2014 256 2015 266 2016 277 Suppose we want to use this data to predict the population in future years. (a) To use the year as a predictor variable, encode 2010 as 1, 2011 as 2, 2012 as 3, etc....
In the 3D Cartesian system the rotation matrix is around the
z-axis is (a 2D rotation):
Where
is the angle to rotate. Then rotation from A to A' is can be
represented via matrix multiplications: [A'] = [R][A]
Such a rotation is useful to return a system solved in
simplified co-ordinates to it's original co-ordinate system,
returning to original meaning to the answer. A full 3D rotation is
simply a series of 2D rotations (with the appropriate matrices)
Question: If...
3 (b) Write the following systems of linear equations as matrix
equation and then as an augmented matrix:
(4marks)
(d) Use Cramer’s rule to solve the system of 2 linear equations
in 3(b). (7marks)
We were unable to transcribe this imageWe were unable to transcribe this image
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...
Problem: Find the matrix which represents in standard coordinates the transformation S : R2 → R2 which shear parallel to the line L ai , where a (3,6) such that a gets transformed into a s, with s (-18,9) Solution The approach we take demonstrates how much convenience can be gained by being able to work with respect to coordinates which are specially adapted to the situation at hand. We compute the matrix S in two steps 1. We find...
Which of the following is the solution to the differential
equation
with the initial condition y(1) = -1/2
A.
B.
C.
D.
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Which of the following is the residual plot for the data in the
given table?
x
1
2
3
4
5
6
y
15
19
18
31
18
31
a)
b)
c)
d)
e) None of the above
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
In the figure (Figure 1), the following EN and XY coordinates for points A through C are given. Determine a 2-D conformal coordinate transformation, to convert the XY coordinates into the EN system. State Plane Coordinates (m) Arbitrary Coordinates (m) Point A 651779.323 290831.221 5804.32 3573.76 B 651369.152 290542.892 3543.59 2773.42 3857.64 3749.59 Figure 〈 1011 〉 Eg-EA アTA Part A What is the scale factor? Express your answer to six significant figures. View Available Hint(s) 8- Submit Part B...
Please answer today! I will upvote/rate.
Best fitting line. Matrix.
5. Predicting Populatioin The data below records the population of Irvine, CA (in thousands of people) for the years 2010-2016: Year Population 220 2010 229 2011 2012 236 2013 247 2014 256 2015 266 2016 277 Suppose we want to use this data to predict the population in future years. (a) To use the year as a predictor variable, encode 2010 as 1, 2011 as 2, 2012 as 3, etc....
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