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Solution's of above examples are given below
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Problem 3: Write the Jacobian matrices of the following mappings and find all points where the...
Please find and classify all the critical points for Q19 and Q20 5-20 Find the local...
Please find and classify all the critical points for Q19 and
Q20
5-20 Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function 5. f(x, y) xy y + y 6. f(x, y)-xy 2x 2y x-y 7. f(x, y) x-y)1 - xy) 8. f(x, y)y(e- ) 9. f(x, y)-x y* + 2xy 10. f(x,...
Please answer C 3. (8 marks total) Show which of the following mappings between real vector spaces are lincar and which...
Please answer C
3. (8 marks total) Show which of the following mappings between real vector spaces are lincar and which are not lincar (a) LRR2 defined by L1(x) (r, 2x). (b) L2 R2 -R2, defined by L2(r, y) (cos(30) -ysin(30), z sin(30) +ycos(30)). (c)L:F(R;R) >R, defined by L()-s()(1) (d) L4 : Cao(R: R) > R, defined by Ldf) =おf(t)dt. (Notes: (i) The real vector space (F(R:R),+) consists of all functions from R to R (i.c. all real-valued functions of...
Please answer D 3. (8 marks total) Show which of the following mappings between real vector spaces are lincar and which...
Please answer D
3. (8 marks total) Show which of the following mappings between real vector spaces are lincar and which are not lincar (a) LRR2 defined by L1(x) (r, 2x). (b) L2 R2 -R2, defined by L2(r, y) (cos(30) -ysin(30), z sin(30) +ycos(30)). (c)L:F(R;R) >R, defined by L()-s()(1) (d) L4 : Cao(R: R) > R, defined by Ldf) =おf(t)dt. (Notes: (i) The real vector space (F(R:R),+) consists of all functions from R to R (i.c. all real-valued functions of...
002 10.0 points Find the Jacobian of the transformation T: (r, 0) + (x, y) when...
002 10.0 points Find the Jacobian of the transformation T: (r, 0) + (x, y) when x = e" cose, y = 2e-" sin . 1. O(x, y) = 2 cos 20 a(r, 0) 2. 8(x, y) a(r, 0j = -3e2r 2(x, y) a(r, 0) = -2 cos 20 4. (x, y) = 2 4. Əlr, o) 5. 0(x, y) = 3er cos 20 5. Ə(r, ) 2(x, y) - 2.21 DA a(r, 0) = -3e4
Question 6 (3 points) a -- 2 points) Find the Jacobian of the transformation the shear...
Question 6 (3 points) a -- 2 points) Find the Jacobian of the transformation the shear transformation: x = au + bv + cw, y=dy + ew, and z fw, where a, b, c, d, e, and f are positive real numbers, and describe the how the volume of the unit cube in uvw coordinates compares to the volume of its transformation in Cartesian coordinates. = b -- 1 point) State one example of a practical application shown in lecture...
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1),...
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 5. Let n N. The goal of this problem is to show that if two real n x n matrices are simil...
Problem 5. Let n N. The goal of this problem is to show that if two real n x n matrices are similar over C, then they are also similar over IK (a) Prove that for all X, y є Rnxn, the function f(t) det (X + ty) is a polynomial in t. (b) Prove that if X and Y are real n × n matrices such that X + ừ is an invertible complex matrix, then there exists a...
dy For a sin(2y) = y cos(2x), find where (20, Yo) = G 3) da |(x0,90)...
dy For a sin(2y) = y cos(2x), find where (20, Yo) = G 3) da |(x0,90) 4'2
21 please inteb CORE 17 20. The matrices in the last two Exercises were the standard...
21 please
inteb CORE 17 20. The matrices in the last two Exercises were the standard matrices of the operators [proji] and refli], respectively, where L is a line through the origin in R2 with unit direction vector (a, b) See Exercise 25 in Section 2.2. Give a geometric argument as to why one of these matrices is invertible and the other matrix is not invertible. Explain also the geometric significance of the inverse of the invertible matrix. For Exercises...
Question 1: (20 points) Find the solution of the initial value problem a = cos? x...
Question 1: (20 points) Find the solution of the initial value problem a = cos? x – sin x – 2y cos x + y2 , y(0) = given that yi(2) = cos x is a solution of the differential equation.
Please find and classify all the critical points for Q19 and
Q20
5-20 Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function 5. f(x, y) xy y + y 6. f(x, y)-xy 2x 2y x-y 7. f(x, y) x-y)1 - xy) 8. f(x, y)y(e- ) 9. f(x, y)-x y* + 2xy 10. f(x,...
Please answer C
3. (8 marks total) Show which of the following mappings between real vector spaces are lincar and which are not lincar (a) LRR2 defined by L1(x) (r, 2x). (b) L2 R2 -R2, defined by L2(r, y) (cos(30) -ysin(30), z sin(30) +ycos(30)). (c)L:F(R;R) >R, defined by L()-s()(1) (d) L4 : Cao(R: R) > R, defined by Ldf) =おf(t)dt. (Notes: (i) The real vector space (F(R:R),+) consists of all functions from R to R (i.c. all real-valued functions of...
Please answer D
3. (8 marks total) Show which of the following mappings between real vector spaces are lincar and which are not lincar (a) LRR2 defined by L1(x) (r, 2x). (b) L2 R2 -R2, defined by L2(r, y) (cos(30) -ysin(30), z sin(30) +ycos(30)). (c)L:F(R;R) >R, defined by L()-s()(1) (d) L4 : Cao(R: R) > R, defined by Ldf) =おf(t)dt. (Notes: (i) The real vector space (F(R:R),+) consists of all functions from R to R (i.c. all real-valued functions of...
002 10.0 points Find the Jacobian of the transformation T: (r, 0) + (x, y) when x = e" cose, y = 2e-" sin . 1. O(x, y) = 2 cos 20 a(r, 0) 2. 8(x, y) a(r, 0j = -3e2r 2(x, y) a(r, 0) = -2 cos 20 4. (x, y) = 2 4. Əlr, o) 5. 0(x, y) = 3er cos 20 5. Ə(r, ) 2(x, y) - 2.21 DA a(r, 0) = -3e4
Question 6 (3 points) a -- 2 points) Find the Jacobian of the transformation the shear transformation: x = au + bv + cw, y=dy + ew, and z fw, where a, b, c, d, e, and f are positive real numbers, and describe the how the volume of the unit cube in uvw coordinates compares to the volume of its transformation in Cartesian coordinates. = b -- 1 point) State one example of a practical application shown in lecture...
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 3: Let f: X -> R, XC R2, be given by f(x, y)n(x 2y 1), V(r,y) e X Find the maximal domain X and write the second-order Taylor polynomial for f around the point (2,1) E X. (6 points)
Problem 5. Let n N. The goal of this problem is to show that if two real n x n matrices are similar over C, then they are also similar over IK (a) Prove that for all X, y є Rnxn, the function f(t) det (X + ty) is a polynomial in t. (b) Prove that if X and Y are real n × n matrices such that X + ừ is an invertible complex matrix, then there exists a...
dy For a sin(2y) = y cos(2x), find where (20, Yo) = G 3) da |(x0,90) 4'2
21 please
inteb CORE 17 20. The matrices in the last two Exercises were the standard matrices of the operators [proji] and refli], respectively, where L is a line through the origin in R2 with unit direction vector (a, b) See Exercise 25 in Section 2.2. Give a geometric argument as to why one of these matrices is invertible and the other matrix is not invertible. Explain also the geometric significance of the inverse of the invertible matrix. For Exercises...
Question 1: (20 points) Find the solution of the initial value problem a = cos? x – sin x – 2y cos x + y2 , y(0) = given that yi(2) = cos x is a solution of the differential equation.
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