Homework Answers
Add Answer to:
2. Suppose that T: Rn → Rm is defined by T,(x)-A, x for each of the...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0,...
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T i...
Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T is the translated set T(p) + T(S) n R What would be the first step in translating p+ S? OA. Rewrite p+ S so that it does not use sets. O B. Rewrite p+S so that it does not use vectors O c. Rewrite p + S as a difference...
a Suppose {יוע ע "ע 3is a linearly dependent set in R. Let T : Rn...
a Suppose {יוע ע "ע 3is a linearly dependent set in R. Let T : Rn Rm be a linear transformation. Explain why { T(L| ), Tjas), Γ(L3 ) must be linearly dependent in Rin. b Suppose (x, t.,) is a linearly independent set in R". Let Tbe a linear transformation. Do T(Li ) , T(L, ), T(ש ) and explain why not. have to be linearly independent in R ? Explain why, or give a counterexample
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax...
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
SF78. Consider the linear map T : Rn → Rm defined by T(v) = Av where...
SF78. Consider the linear map T : Rn → Rm defined by T(v) = Av where A=12 43 6 12-7 (a) What is m? (b) What is n? (c) The image of T is a subspace of R. What is i? (d) The image of T is isomorphic to R. What is j? e The kermel of T is isomorphic to Rt. What is k7 (f) The kernel of T is a subspace of R. What is ?
Problem 4. Let GL2(R) be the vector space of 2 x 2 square matrices with usual matrix addition and...
Problem 4. Let GL2(R) be the vector space of 2 x 2 square matrices with usual matrix addition and scalar multiplication, and Wー State the incorrect statement from the following five 1. W is a subspace of GL2(R) with basis 2. W -Ker f, where GL2(R) R is the linear transformation defined by: 3. Given the basis B in option1. coordB( 23(1,2,2) 4. GC2(R)-W + V, where: 5. Given the basis B in option1. coordB( 2 3 (1,2,3) Problem 5....
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by...
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0,...
Problem 5. Given vi,v2,... ,Vm R", let RRm be defined by f(x)-x, v1), x, v2), (x, Vm where (x' y)...
Problem 5. Given vi,v2,... ,Vm R", let RRm be defined by f(x)-x, v1), x, v2), (x, Vm where (x' y) is the standard inner product of Rn Which of the following statement is incorrect? 1. Taking the standard bases Un on R": codomain: MatUn→Un(f)-(v1 2. Taking the standard bases Un on R: codomain: v2 vm) Matf)- 3. f is a linear transformation. 4. Kerf- x E Rn : Vx = 0 , where: Problem 8. Which of the following statements...
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homoge...
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homogeneous coordinates are frequently used to represent affine functions in robotics and 3D graphics. We define the function H by and if f-x) Mxtt where then C0 a. Some vectors are valid homogeneous representations of vectors, and some are not. Explain how to tell if some vector y-0 is the homogeneous representation of some other vector -y...
#3 Only In the following 4, let V be a vector space, and assume B- [bi,...,...
#3 Only
In the following 4, let V be a vector space, and assume B- [bi,..., bn^ is a basis for V. These 4 problems, taken together, give a complete argument that the coordinate mapping Фв : V → Rn defined by sending a vector v E V to its coordinate vector [v]в є Rn is an isomorphism between V and Rn. In other words, Фв : V-> Rn is a well- defined linear transformation that is one-to-one and onto....
Let A be an m × n matrix, let x Rn and let 0 be the zero vector in Rm. (a) Let u, v є Rn be any two solutions of Ax 0, and let c E R. Use the properties of matrix-vector multiplication to show that u+v and cu are also solutions of Ax O. (b) Extend the result of (a) to show that the linear combination cu + dv is a solution of Ax 0 for any c,d...
Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T is the translated set T(p) + T(S) n R What would be the first step in translating p+ S? OA. Rewrite p+ S so that it does not use sets. O B. Rewrite p+S so that it does not use vectors O c. Rewrite p + S as a difference...
a Suppose {יוע ע "ע 3is a linearly dependent set in R. Let T : Rn Rm be a linear transformation. Explain why { T(L| ), Tjas), Γ(L3 ) must be linearly dependent in Rin. b Suppose (x, t.,) is a linearly independent set in R". Let Tbe a linear transformation. Do T(Li ) , T(L, ), T(ש ) and explain why not. have to be linearly independent in R ? Explain why, or give a counterexample
(12) (after 3.3) (a) Find a linear transformation T. Rº Rº such that T(x) = Ax that reflects a vector (1), 12) about the Tz-axis. (b) Find a linear transformation SR2 R2 such that T(x) = Bx that rotates a vector (2, 2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the matrix of this transformation explicitly. How...
SF78. Consider the linear map T : Rn → Rm defined by T(v) = Av where A=12 43 6 12-7 (a) What is m? (b) What is n? (c) The image of T is a subspace of R. What is i? (d) The image of T is isomorphic to R. What is j? e The kermel of T is isomorphic to Rt. What is k7 (f) The kernel of T is a subspace of R. What is ?
Problem 4. Let GL2(R) be the vector space of 2 x 2 square matrices with usual matrix addition and scalar multiplication, and Wー State the incorrect statement from the following five 1. W is a subspace of GL2(R) with basis 2. W -Ker f, where GL2(R) R is the linear transformation defined by: 3. Given the basis B in option1. coordB( 23(1,2,2) 4. GC2(R)-W + V, where: 5. Given the basis B in option1. coordB( 2 3 (1,2,3) Problem 5....
25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R – RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0,...
Problem 5. Given vi,v2,... ,Vm R", let RRm be defined by f(x)-x, v1), x, v2), (x, Vm where (x' y) is the standard inner product of Rn Which of the following statement is incorrect? 1. Taking the standard bases Un on R": codomain: MatUn→Un(f)-(v1 2. Taking the standard bases Un on R: codomain: v2 vm) Matf)- 3. f is a linear transformation. 4. Kerf- x E Rn : Vx = 0 , where: Problem 8. Which of the following statements...
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homogeneous coordinates are frequently used to represent affine functions in robotics and 3D graphics. We define the function H by and if f-x) Mxtt where then C0 a. Some vectors are valid homogeneous representations of vectors, and some are not. Explain how to tell if some vector y-0 is the homogeneous representation of some other vector -y...
#3 Only
In the following 4, let V be a vector space, and assume B- [bi,..., bn^ is a basis for V. These 4 problems, taken together, give a complete argument that the coordinate mapping Фв : V → Rn defined by sending a vector v E V to its coordinate vector [v]в є Rn is an isomorphism between V and Rn. In other words, Фв : V-> Rn is a well- defined linear transformation that is one-to-one and onto....
Most questions answered within 3 hours.
-
"The Ramsey family has total assets of $1,000,000 and total
liabilities of $700,000. Included in their...
asked 8 minutes ago -
The following table gives information on the amount of sugar (in
grams) and the calorie count...
asked 1 hour ago -
A car travels at an average speed of 56 mph for 15 hours. What
was the...
asked 1 hour ago -
Exercise on Mirror, Mirror on the Wall/lnitial Self
Evaluation
Write an Initial Self Evaluation paper that...
asked 2 hours ago -
Implementation of policy recommendations is often a
problem. What do you see as the major barriers...
asked 4 hours ago -
23- The consideration needed to support a contract
must:
a. Flow to the promise AND have...
asked 5 hours ago -
1. What is the main causal factor of Border line personality
disorder? Research has also found...
asked 7 hours ago -
The National Institute of Standards and Technology (NIST)
supplies "standard materials" whose physical properties are
supposed...
asked 8 hours ago -
Alpha Centauri A and B are Sun-like stars, and together they
form the binary star Alpha...
asked 8 hours ago -
What is the pH of a 0.200 M solution of sulfurous acid? Given:
Ka1 = 1.70×10–2,...
asked 8 hours ago -
Sociologists have conducted much interesting research on gender
stereotypes in American society. A curious aspect of...
asked 8 hours ago -
1. Based on your results, calculate how many kilograms of plant
material you would need to...
asked 8 hours ago