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Q1 17 Points Let T: M2x2(R) P2(R), H (2a +b)x2 + (6 – c)x +(c –...
Q1 17 Points Let T: M2x2(R) P2(R), H (2a +b)x2 + (6 – c)x +(c – 3d). Let B = (16 0) (0 :), (1 o) 9)) = (6 7')(*: -) ) 6 :-)) B' = C = (x2,æ, 1) C'= (x + 2, x + 3, x2 – 2x – 6). You may assume that all of the above are bases for the corresponding vector spaces. Q1.1 2 Points Show that T is linear. Q1.2 9 Points Compute [T),...
71121 4 1 15 Let S = -21,-1, 3 and C = | 1,2], o be...
71121 4 1 15 Let S = -21,-1, 3 and C = | 1,2], o be bases for R'. Find the change-of- L5 JL-1] [4] IL-5] [ 8 7 ] coordinates matrix from B to C and the change-of-coordinates matrix from C to B. Find [x]. for x, = 4b, - 2b, +3b,. Find [x], for x, = 4c, - 2c, + 3e, Show these work by finding the coordinates of each vector in the standard basis using Band C
Show that T is linear Q1 17 Points Let b T: M2x2(R) + P2 (R), H...
Show that T is linear
Q1 17 Points Let b T: M2x2(R) + P2 (R), H (2a+b)x2 + (b – c)x+(c – 3d). с d Let 1 0 0 0 B = (( b); C8 1 0 0 0 0 1 :)C. 11), 1) (7.1)) i), (6 ;)) 1 0 1 B = (CO 2 -1 1 1 1 C = (x², x, 1) C' = (x + 2, x + 3, x2 – 2x – You may assume that...
[ 5 2 31 8. (9 points) Let M = 3 8 3 . ( 2...
[ 5 2 31 8. (9 points) Let M = 3 8 3 . ( 2 0 4] -11 | 3 | a. Show that uj = 0 , 12 = -3 , uz = 6 are eigenvectors of M, and 1 1 1 determine the corresponding eigenvalues. b. Using your answer to part (a) what is det(M)? c. Using your answer to part (a), what is the characteristic polynomial of M? d. Using your answer to part (a), is...
8. (13 points) Let g(x) = /3 + x2. (a) Find Ti (r), the first Taylor polynomial for g(x) based at b 1 (b) Use your ans...
8. (13 points) Let g(x) = /3 + x2. (a) Find Ti (r), the first Taylor polynomial for g(x) based at b 1 (b) Use your answer to (a) to approximate the value of 3.25 (c) Use Taylor's inequality to find an upper bound for the error in your approximation in part (b) 8. (a) Ti(r)2 +3(x - 1) (b) 3.25 g(0.5) Ti(0.5) = 1.75 (c) HINT: |g"(x)| = 3 + x2)3/2° This is positive and decreasing on [0.5, 1]....
Let D P3P3 be the function that sends a polynomial of degree 3 to its derivative...
Let D P3P3 be the function that sends a polynomial of degree 3 to its derivative (a) Find an eigenvector for D or explain why no eigenvector exists Write your solution here (b) Let B 1 x, x + x2, x2 + x3,x3}. B is a basis for P3. Find MDB-B Here, MD.- is the unique matrix such that MD-xs = [D(x)]s Write your solution here Recall that D: P is polynomial differentiation. 1x, x +x2, x2 +x3,x3} and C...
You should test out your script using the following matrices. 2 3 1 2 3 1 C D- 3 2 B- A- -3 8 4 8 2 4 4 1 You may n...
You should test out your script using the following matrices. 2 3 1 2 3 1 C D- 3 2 B- A- -3 8 4 8 2 4 4 1 You may not use any special MATLAB tools. Instead, work symbolically and derive general expressions for the eigenvalues and the eigenvectors. For instance, you may not use the SOLVE function. If you are not sure whether or not a particular function is available to you, just ask Include your hand...
answer all and show work please. clear hand writing please 1. (6 points) Let f(x) =...
answer all and show work please. clear hand writing
please
1. (6 points) Let f(x) = -x2 - 2x + 3. (a) Does the graph of f(x) open upward or downward? Justify your answer. 6) Algebraically find the vertex and axis of symmetry of f(x). Report each answer as an ordered pair and equation, respectively, Vertex Axis of Symmetry: (C) Algebraically find the X- and y-intercepts of f(x). Report your answer(s) as an ordered pair(s). x-intercepts: y-intercept: (a) Using parts...
1. Let u be a solution of the wave equation u0. Let the points A, B, C, D be the vertices of the ...
1. Let u be a solution of the wave equation u0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines z--d-q,z-ct-c2, z + ct = di, z + ct d2. Show that u(A) u (C) u(B) +u(D) Use this to find u satisfying till- tLzz =0, u( s,s)-s, u(8,8)-82 for s > 0. For which (r, t) can you determine u (x, t) uniquely this way?
1. Let...
a = 1 b = 2 c= 3 Let a, b and c be the three...
a = 1
b = 2
c= 3
Let a, b and c be the three integers previously assigned to you. Let q be the three-digit number abc. The shape, y(x), of a certain structure is governed by the following differential equation. 1 dy dx? x dx Suppose that y(0.5)=0.71459 y(3)=4 + 1. Use the shooting method and MATLAB's built-in numerical solver ODE45 to compute y(x) on the interval 0.55x53. (The value of y at x = 3 must be...
Q1 17 Points Let T: M2x2(R) P2(R), H (2a +b)x2 + (6 – c)x +(c – 3d). Let B = (16 0) (0 :), (1 o) 9)) = (6 7')(*: -) ) 6 :-)) B' = C = (x2,æ, 1) C'= (x + 2, x + 3, x2 – 2x – 6). You may assume that all of the above are bases for the corresponding vector spaces. Q1.1 2 Points Show that T is linear. Q1.2 9 Points Compute [T),...
71121 4 1 15 Let S = -21,-1, 3 and C = | 1,2], o be bases for R'. Find the change-of- L5 JL-1] [4] IL-5] [ 8 7 ] coordinates matrix from B to C and the change-of-coordinates matrix from C to B. Find [x]. for x, = 4b, - 2b, +3b,. Find [x], for x, = 4c, - 2c, + 3e, Show these work by finding the coordinates of each vector in the standard basis using Band C
Show that T is linear
Q1 17 Points Let b T: M2x2(R) + P2 (R), H (2a+b)x2 + (b – c)x+(c – 3d). с d Let 1 0 0 0 B = (( b); C8 1 0 0 0 0 1 :)C. 11), 1) (7.1)) i), (6 ;)) 1 0 1 B = (CO 2 -1 1 1 1 C = (x², x, 1) C' = (x + 2, x + 3, x2 – 2x – You may assume that...
[ 5 2 31 8. (9 points) Let M = 3 8 3 . ( 2 0 4] -11 | 3 | a. Show that uj = 0 , 12 = -3 , uz = 6 are eigenvectors of M, and 1 1 1 determine the corresponding eigenvalues. b. Using your answer to part (a) what is det(M)? c. Using your answer to part (a), what is the characteristic polynomial of M? d. Using your answer to part (a), is...
8. (13 points) Let g(x) = /3 + x2. (a) Find Ti (r), the first Taylor polynomial for g(x) based at b 1 (b) Use your answer to (a) to approximate the value of 3.25 (c) Use Taylor's inequality to find an upper bound for the error in your approximation in part (b) 8. (a) Ti(r)2 +3(x - 1) (b) 3.25 g(0.5) Ti(0.5) = 1.75 (c) HINT: |g"(x)| = 3 + x2)3/2° This is positive and decreasing on [0.5, 1]....
Let D P3P3 be the function that sends a polynomial of degree 3 to its derivative (a) Find an eigenvector for D or explain why no eigenvector exists Write your solution here (b) Let B 1 x, x + x2, x2 + x3,x3}. B is a basis for P3. Find MDB-B Here, MD.- is the unique matrix such that MD-xs = [D(x)]s Write your solution here Recall that D: P is polynomial differentiation. 1x, x +x2, x2 +x3,x3} and C...
You should test out your script using the following matrices. 2 3 1 2 3 1 C D- 3 2 B- A- -3 8 4 8 2 4 4 1 You may not use any special MATLAB tools. Instead, work symbolically and derive general expressions for the eigenvalues and the eigenvectors. For instance, you may not use the SOLVE function. If you are not sure whether or not a particular function is available to you, just ask Include your hand...
answer all and show work please. clear hand writing
please
1. (6 points) Let f(x) = -x2 - 2x + 3. (a) Does the graph of f(x) open upward or downward? Justify your answer. 6) Algebraically find the vertex and axis of symmetry of f(x). Report each answer as an ordered pair and equation, respectively, Vertex Axis of Symmetry: (C) Algebraically find the X- and y-intercepts of f(x). Report your answer(s) as an ordered pair(s). x-intercepts: y-intercept: (a) Using parts...
1. Let u be a solution of the wave equation u0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines z--d-q,z-ct-c2, z + ct = di, z + ct d2. Show that u(A) u (C) u(B) +u(D) Use this to find u satisfying till- tLzz =0, u( s,s)-s, u(8,8)-82 for s > 0. For which (r, t) can you determine u (x, t) uniquely this way?
1. Let...
a = 1
b = 2
c= 3
Let a, b and c be the three integers previously assigned to you. Let q be the three-digit number abc. The shape, y(x), of a certain structure is governed by the following differential equation. 1 dy dx? x dx Suppose that y(0.5)=0.71459 y(3)=4 + 1. Use the shooting method and MATLAB's built-in numerical solver ODE45 to compute y(x) on the interval 0.55x53. (The value of y at x = 3 must be...
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