Homework Answers
Add Answer to:
Let T є L(C3) be defined by T(r, y, z)-(y-2-2c, z-2-2y,1-2y-22). (a) Is span((1,1,1)) invariant under...
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2-R2 be defined by f(x,y) = (y,z), then find al...
please answer both a and b
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2-R2 be defined by f(x,y) = (y,z), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation. (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V V such that U is not an invariant subspace of f. Hence, or otherwise, show that: a vector subspace U-o or...
Consider the three-dimensional subspace of function space defined by the span of 1, r, and a2 the...
Consider the three-dimensional subspace of function space defined by the span of 1, r, and a2 the first three orthogonal polynomials on -1,1. Let f(x) 21, and consider the subset G-{g(z) | 〈f,g〉 0), the set of functions orthogonal to f using the L inner product on, (This can be thought of as the plane normal to f(x) in the three-dimensional function space.) Let h(z) 2-1. Find the function g(x) є G in the plane which is closest to h(x)....
2. Define g(r, y,z) = 22 sin(y - rz) 2y. Answer the following questions (a) Compute...
2. Define g(r, y,z) = 22 sin(y - rz) 2y. Answer the following questions (a) Compute the gradient of g at the point P (1,1,1) (b) The point P defined above is on the level surface g = C. What is the value of C? (c) Find an equation of the tangent plane to the level surface g C at the point P (d) Suppose we want to travel from the point P to the level surface g = C...
5. Let V = {(x + 2y, x + 2y) : x,y,z E R} be a...
5. Let V = {(x + 2y, x + 2y) : x,y,z E R} be a subspace of R2, Find dim V.
= Let T:R3 → Rº be the linear transformation given by T(x,y,z) = (x – 2,...
= Let T:R3 → Rº be the linear transformation given by T(x,y,z) = (x – 2, x + y, x + y + 2z) for all (x,y,z) e R3. Determine whether T is invertible or not. If T is invertible, find the inverse of T and compute inverse image of (1,1,1) under T.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/...
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
please answer both!! thank you 6. Is the transformation T: R → R defined T(x, y)...
please answer both!! thank you
6. Is the transformation T: R → R defined T(x, y) = (x + y, x - y + 1) a linear transformation? [3 marks] 8. Let A = 5 6 Find the eigenvalues and ONE of the corresponding 21 eigenvectors of A. [5 marks]
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of th...
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of the zy-plane, bounded below by the surface ะ1-sin|cos y and above by the sur- 2) face of elliptical paraboloid 22-2-4-9
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of the zy-plane, bounded below by the surface ะ1-sin|cos y and above by the sur-...
detail steps please 1· Let L:R'→R' bedefined by L(x,y)-(x-2y,x+2y Let S- (1.-1).(0.D)be a basis for R'...
detail steps please
1· Let L:R'→R' bedefined by L(x,y)-(x-2y,x+2y Let S- (1.-1).(0.D)be a basis for R' and let T be the natural basis for IR2 Find the matrix representing L w. r to a) S b) Sand T c T andS d) T e) Compute L(2,-1) using the definition of L and also using the matrices obtained in a), b), c)and d)
please answer both a and b
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2-R2 be defined by f(x,y) = (y,z), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation. (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V V such that U is not an invariant subspace of f. Hence, or otherwise, show that: a vector subspace U-o or...
Consider the three-dimensional subspace of function space defined by the span of 1, r, and a2 the first three orthogonal polynomials on -1,1. Let f(x) 21, and consider the subset G-{g(z) | 〈f,g〉 0), the set of functions orthogonal to f using the L inner product on, (This can be thought of as the plane normal to f(x) in the three-dimensional function space.) Let h(z) 2-1. Find the function g(x) є G in the plane which is closest to h(x)....
2. Define g(r, y,z) = 22 sin(y - rz) 2y. Answer the following questions (a) Compute the gradient of g at the point P (1,1,1) (b) The point P defined above is on the level surface g = C. What is the value of C? (c) Find an equation of the tangent plane to the level surface g C at the point P (d) Suppose we want to travel from the point P to the level surface g = C...
5. Let V = {(x + 2y, x + 2y) : x,y,z E R} be a subspace of R2, Find dim V.
= Let T:R3 → Rº be the linear transformation given by T(x,y,z) = (x – 2, x + y, x + y + 2z) for all (x,y,z) e R3. Determine whether T is invertible or not. If T is invertible, find the inverse of T and compute inverse image of (1,1,1) under T.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
please answer both!! thank you
6. Is the transformation T: R → R defined T(x, y) = (x + y, x - y + 1) a linear transformation? [3 marks] 8. Let A = 5 6 Find the eigenvalues and ONE of the corresponding 21 eigenvectors of A. [5 marks]
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of the zy-plane, bounded below by the surface ะ1-sin|cos y and above by the sur- 2) face of elliptical paraboloid 22-2-4-9
Evaluate the integral: (x) dzdrdy, where B is the cylinder over the rectangular region R-(z, y) є R2 :-1 z 1,-2 y of the zy-plane, bounded below by the surface ะ1-sin|cos y and above by the sur-...
detail steps please
1· Let L:R'→R' bedefined by L(x,y)-(x-2y,x+2y Let S- (1.-1).(0.D)be a basis for R' and let T be the natural basis for IR2 Find the matrix representing L w. r to a) S b) Sand T c T andS d) T e) Compute L(2,-1) using the definition of L and also using the matrices obtained in a), b), c)and d)
Most questions answered within 3 hours.
-
Create a 32-run crossed array design with six control factors
and two noise factors such that...
asked 44 minutes ago -
A 500g sample of sand from source A has the following amounts
retained on each sieve....
asked 46 minutes ago -
In
your own words, please explain the essay by John Keynes wrote "The
End of Laissez...
asked 45 minutes ago -
How are the matrix and pixels related? Why are smaller
pixels better for diagnostic quality?
asked 48 minutes ago -
2. An AC generator has 80 rectangular loops on
its armature. Each loop is 11 cm...
asked 49 minutes ago -
Please help me with this question. Consider Aldi’s current and
potential geographic markets (see Exhibit 4...
asked 52 minutes ago -
What are the main components of the fermentation process and
give an explanation of each? Include...
asked 1 hour ago -
Explain which types of cells in the body (belonging to which
organs, etc.) are sensitive to...
asked 1 hour ago -
A single cable supports an 703-kg elevator car. What is the
tension in the cable when...
asked 1 hour ago -
among the three different ways to link CSS specifications to an
HTML document (inline CSS, document...
asked 1 hour ago -
(1) Write the net ionic equation for the reaction that occurs
when equal volumes of 0.191...
asked 2 hours ago -
On the night of April 18, 1775, a signal was to be sent from the
Old...
asked 1 hour ago