Homework Answers
Let x = [xı x2 x3], and let TER → R be the linear transformation defined...
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space of dimension 2. What is the dimension of the row space of A? Not enough information has been given. O 1/2 3 2. Question 16 (2 points) The rank of the matrix 1 2 - 1 2 4 2 1 2 3 is 02 O none of the given options Question 15 (2 points) Which of the following is not a vector space because...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
can you explain the process please. (1 point) Let f: R2R be the linear transformation defined...
can you explain the process
please.
(1 point) Let f: R2R be the linear transformation defined by 3 -4 f(x)-2 4 X. Let be two different bases for R a Find the matrix If1 for f relative to the basis B -70 AIB -26 b. Find the matrix iE for f relative to the basis C c. Find the transition matrix [TE from Cto B LIE
(1 point) Let f: R3 R3 be the linear transformation defined by f(3) = [ 2...
(1 point) Let f: R3 R3 be the linear transformation defined by f(3) = [ 2 1 1-4 -2 -57 -5 -4 7. 0 -2 Let B C = = {(2,1, -1),(-2,-2,1),(-1, -2, 1)}, {(-1,1,1),(1, -2, -1),(-1,3, 2)}, be two different bases for R. Find the matrix (fls for f relative to the basis B in the domain and C in the codomain. [] =
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y)...
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y) = (3y, 22 – y). Suppose further that ^ C R2 is a curve in R2 consisting of the parabola y = 22 - 1 for 1 € (-1,0) and the straight line y = 1 – 1 for 1 € [0,1]. (i) Sketch the curvey in R2 [2] (ii) By considering the curve y piecewise, compute the vector field integral: [5] F(x). F(x)...
(c) Let f : IR2 -R2 be given by f(x,)= (a1)2-y1, (-12) Let S, S' be...
(c) Let f : IR2 -R2 be given by f(x,)= (a1)2-y1, (-12) Let S, S' be the subsets of R2 as indicated in the picture below. Prove that f maps S onto S' (0,1) v-axis V=1 (2,1) (1,1) y =(x-1)2 у-ахis u 1 v=u-1 u-axis (1,0) (0,0) х-аxis (1,0)
(c) Let f : IR2 -R2 be given by f(x,)= (a1)2-y1, (-12) Let S, S' be the subsets of R2 as indicated in the picture below. Prove that f maps S...
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 :...
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
Let T be the linear transformation from R3 into R2 defined by (1) For the standard...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
1. Let f(x) be the 2T-periodic function which is defined by f(xcos(x/4) for -<< (a) Draw the graph of y = f(x) over the interval-3r < x < 3π. Is f continuous on R? (b) Find the trigonomet...
1. Let f(x) be the 2T-periodic function which is defined by f(xcos(x/4) for -<< (a) Draw the graph of y = f(x) over the interval-3r < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L = π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: and , and 162 16k2-1" 16k2 1)2 に1...
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space of dimension 2. What is the dimension of the row space of A? Not enough information has been given. O 1/2 3 2. Question 16 (2 points) The rank of the matrix 1 2 - 1 2 4 2 1 2 3 is 02 O none of the given options Question 15 (2 points) Which of the following is not a vector space because...
Let x = [X1 X2 X3], and let T:R3 → R3 be the linear transformation defined by x1 + 5x2 – x3 T(x) - X2 x1 + 2x3 Let B be the standard basis for R3 and let B' = {V1, V2, V3}, where 4 4. ---- 4 and v3 -- 4 Find the matrix of T with respect to the basis B, and then use Theorem 8.5.2 to compute the matrix of T with respect to the basis B”....
can you explain the process
please.
(1 point) Let f: R2R be the linear transformation defined by 3 -4 f(x)-2 4 X. Let be two different bases for R a Find the matrix If1 for f relative to the basis B -70 AIB -26 b. Find the matrix iE for f relative to the basis C c. Find the transition matrix [TE from Cto B LIE
(1 point) Let f: R3 R3 be the linear transformation defined by f(3) = [ 2 1 1-4 -2 -57 -5 -4 7. 0 -2 Let B C = = {(2,1, -1),(-2,-2,1),(-1, -2, 1)}, {(-1,1,1),(1, -2, -1),(-1,3, 2)}, be two different bases for R. Find the matrix (fls for f relative to the basis B in the domain and C in the codomain. [] =
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y) = (3y, 22 – y). Suppose further that ^ C R2 is a curve in R2 consisting of the parabola y = 22 - 1 for 1 € (-1,0) and the straight line y = 1 – 1 for 1 € [0,1]. (i) Sketch the curvey in R2 [2] (ii) By considering the curve y piecewise, compute the vector field integral: [5] F(x). F(x)...
(c) Let f : IR2 -R2 be given by f(x,)= (a1)2-y1, (-12) Let S, S' be the subsets of R2 as indicated in the picture below. Prove that f maps S onto S' (0,1) v-axis V=1 (2,1) (1,1) y =(x-1)2 у-ахis u 1 v=u-1 u-axis (1,0) (0,0) х-аxis (1,0)
(c) Let f : IR2 -R2 be given by f(x,)= (a1)2-y1, (-12) Let S, S' be the subsets of R2 as indicated in the picture below. Prove that f maps S...
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
1. Let f(x) be the 2T-periodic function which is defined by f(xcos(x/4) for -<< (a) Draw the graph of y = f(x) over the interval-3r < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L = π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: and , and 162 16k2-1" 16k2 1)2 に1...
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