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Quiz 8 Please show all your work to receive full credits. 1) Show that v is...
Show all your work for full credits. Check your answer. 1. Find an equation of the...
Show all your work for full credits. Check your answer. 1. Find an equation of the plane through P (5,0,-3) that is parallel to the given plane: 4x – y + 3z – 9 = 0 4x – y + 3z – 9 = 0 P (5,0,-3)
In order to receive full credit on these problems, you must clearly show all your work....
In order to receive full credit on these problems, you must clearly show all your work. An answer without justification will receive 0 credit. 1. (10 marks) Consider the subspace V = Span 11 [2] 5] - 1 [5] -71 [1] doo (a) Find a basis for V and V. (b) Find dim(V) and dim(V+). (c) Find a matrix B satisfying V = null(B). 2. (2 marks) True or False: If E is an elementary matrix, then nullity(A) = nullity(EA)....
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue...
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
Show all steps clearly, to receive full marks for your solutions. 10. For each of the...
Show all steps clearly, to receive full marks for your solutions. 10. For each of the following, identify the base function and describe the transformation(s): F(x+1) f(x) = -4(3x)" + 5 (8 marks) 11. Describe the transformations that must be applied to the graph of the base function fee) to obtain the transformed function. Write the transformed equation in simplified form. $12)=x, y21-- 1)) + 1 (10 marks) State the base function that corresponds to the transformed lunction = -21...
Please solve #4 Solve problems below, Please show ALL your work! You will receive full credit...
Please solve #4
Solve problems below, Please show ALL your work! You will receive full credit only if you show all the appropriate steps. 1. In the problem below complete sentence in the definition of limit: Let (an) is a sequence. Number A is a limit of the sequence fan if for any 0 exists Ne such that Directly from this definition using e- N language prove that 1L lim -= n→oo n + 1000 3. cos n 5n2 +...
Please show complete and neat steps for all the problems 8. The eigenvalues and corresponding eigenvectors for this...
Please show complete and neat steps for all the problems
8. The eigenvalues and corresponding eigenvectors for this matrix are given below. 1 -3 1 b+3c a) Verify that these are indeed the correct and valid eigenvector/eigenvalue combinations for this matrix. x(t) y(t) z(t) Give the complete solution to the differential equation X'- AX, where X b) Please give your answers for x(t), y(t), and z(t) explicitly. solvé if you dont
8. The eigenvalues and corresponding eigenvectors for this matrix...
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v...
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v ER is a nonzero column vector. Let A (a) Show that v is an eigenvector of A correspond zero column vector. Let A be the n xn matrix vvT. n eigenvector of A corresponding to eigenvalue = |v||2. lat O is an eigenvalue of multiplicity n - 1. (Hint: What is rank A?) (b) Show that 0 is an eigenvalue of
Show all steps clearly, to receive full marks for your solutions. 10. For each of the...
Show all steps clearly, to receive full marks for your solutions. 10. For each of the following, identify the base function and describe the transformation(s): Fle) = P(x + 1) f(x) = -4(3x)* + 5 (8 marks) 11. 12. Describe the transformations that must be applied to the graph of the base function (3) to obtain the transformed function. Write the transformed equation in simplified form. f(x) = x, y=71-5 (x - 1)) + 1 (10 marks) State the base...
Practice Problem 5.16 (to receive full credit, please show all your work in a professional Vehicles...
Practice Problem 5.16 (to receive full credit, please show all your work in a professional Vehicles begin to arrive at a parking lot at 0:00 A.M. at a rat to arrive at a parking lot at 6:00 A.M. at a rate 8 per minute. Due to an accident on the access highway, no arrive from 6:20 to 6:30 A.M. From 6:30 A.M. on, vehicles arrive at a rate of 2 per minute. The parking lot attendant processes incoming vehicles (colloots...
please help !!!! 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalu...
please help !!!!
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
Show all your work for full credits. Check your answer. 1. Find an equation of the plane through P (5,0,-3) that is parallel to the given plane: 4x – y + 3z – 9 = 0 4x – y + 3z – 9 = 0 P (5,0,-3)
In order to receive full credit on these problems, you must clearly show all your work. An answer without justification will receive 0 credit. 1. (10 marks) Consider the subspace V = Span 11 [2] 5] - 1 [5] -71 [1] doo (a) Find a basis for V and V. (b) Find dim(V) and dim(V+). (c) Find a matrix B satisfying V = null(B). 2. (2 marks) True or False: If E is an elementary matrix, then nullity(A) = nullity(EA)....
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
Show all steps clearly, to receive full marks for your solutions. 10. For each of the following, identify the base function and describe the transformation(s): F(x+1) f(x) = -4(3x)" + 5 (8 marks) 11. Describe the transformations that must be applied to the graph of the base function fee) to obtain the transformed function. Write the transformed equation in simplified form. $12)=x, y21-- 1)) + 1 (10 marks) State the base function that corresponds to the transformed lunction = -21...
Please solve #4
Solve problems below, Please show ALL your work! You will receive full credit only if you show all the appropriate steps. 1. In the problem below complete sentence in the definition of limit: Let (an) is a sequence. Number A is a limit of the sequence fan if for any 0 exists Ne such that Directly from this definition using e- N language prove that 1L lim -= n→oo n + 1000 3. cos n 5n2 +...
Please show complete and neat steps for all the problems
8. The eigenvalues and corresponding eigenvectors for this matrix are given below. 1 -3 1 b+3c a) Verify that these are indeed the correct and valid eigenvector/eigenvalue combinations for this matrix. x(t) y(t) z(t) Give the complete solution to the differential equation X'- AX, where X b) Please give your answers for x(t), y(t), and z(t) explicitly. solvé if you dont
8. The eigenvalues and corresponding eigenvectors for this matrix...
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v ER is a nonzero column vector. Let A (a) Show that v is an eigenvector of A correspond zero column vector. Let A be the n xn matrix vvT. n eigenvector of A corresponding to eigenvalue = |v||2. lat O is an eigenvalue of multiplicity n - 1. (Hint: What is rank A?) (b) Show that 0 is an eigenvalue of
Show all steps clearly, to receive full marks for your solutions. 10. For each of the following, identify the base function and describe the transformation(s): Fle) = P(x + 1) f(x) = -4(3x)* + 5 (8 marks) 11. 12. Describe the transformations that must be applied to the graph of the base function (3) to obtain the transformed function. Write the transformed equation in simplified form. f(x) = x, y=71-5 (x - 1)) + 1 (10 marks) State the base...
Practice Problem 5.16 (to receive full credit, please show all your work in a professional Vehicles begin to arrive at a parking lot at 0:00 A.M. at a rat to arrive at a parking lot at 6:00 A.M. at a rate 8 per minute. Due to an accident on the access highway, no arrive from 6:20 to 6:30 A.M. From 6:30 A.M. on, vehicles arrive at a rate of 2 per minute. The parking lot attendant processes incoming vehicles (colloots...
please help !!!!
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
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