In Problems 1-9, consider the given vector x. Find the vectors that result from each of the follo...
5. (3) Let X = Serie x = ()m - (*) indo 3 x 3 mais Find a 3 x 3 matrix A such that the projection PAX = e vector X ER projected onto the line I that is parallel to a and passes through the origin. Pex - Ax 6. (4) The line l in Ris given by the equation x + 3y = 0. (a) What is the angle e between the positive x-axis and the line...
(1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through an angle of 90 in the clockwise direction C. Projection onto the y-axis D. Reflection in the y-axis E. Rotation through an angle of 90° in the counterclockwise direction -1 0 0.5 0 0 0.5 0 -1 F. Reflection in the r-axis 0 -1 (1 point) Match each linear transformation with its matrix. A. Contraction by a factor of2 B. Rotation through...
5.4. Find the matrix of the orthogonal projection in R2 onto the line x1 = –2x2. Hint: What is the matrix of the projection onto the coordinate axis x1? Problem 5. Problem 5.4 on page 23. The following method is suggested: (1) Find an angle o such that the line x1 = –2x2 is obtained by rotating the x-axis by 0. (2) Convince yourself with geometry that to project a vector v onto the line x1 = –2x2 is the...
#1 Exercises with Vectors-II Name [1] Suppose you have two vectors, a and b, that have the same length, so that lal-lb but they point in different directions. Denote the angle between them by . Show that tan(0/2) la-bMa+b Hint: Compute the right-hand side using the fact that lal-bl, and the trig identities 1-cos θ-2sin'(9/2) and 1+cos9-2cos(θ/2) 12] Vectors in 3-dimensions are often parameterized in terms of their length and two angles, as shown in the figure (think of a...
cos2 θ The transformationPez, cos θ sin θ 2 gives the orthogonal projection of the vector,2 onto ortho cosesin θ sin2 θ | the line through the origin that makes the angle θ with the x-axis. Find the projection of'l,6] onto the line through the origintht makes an angle Give your answer to 2 decimal places. The vector- 334,103 Preview Points possible: 1 Unlimited attempts. Score on last attempt: 0. Score in gradebook: 0 Message instructor about this question Post...
For each of the following, find the standard matrix of the given transformation from R2 to R2 (a) Counterclockwise rotation through 120 about the origin. sin (a) f дх Ω (b) Projection onto the line y 5 x. sin (a) Ω да (c) Reflection in the line y= x- sin (a) Ω f
(1 point) Match each linear transformation with its matrix. ? 1 10 A. Identity transformation B. Projection onto the x-axis 0 C. Rotation by 180' Di D. Dilation by a factor of 2 E. Reflection in the y-axis F. Projection onto the y-axis ? 5 s[:] golo [ ] ?
For each of the following, find the standard matrix of the given transformation from R2 to R2. (a) Clockwise rotation through 30° about the origin. a ab sin(a) 22 ar (b) Projection onto the line y = -42. a ab sin(a) !!! 22 8 (c) Reflection in the line y = 1 a ab sin(a) 22 ? Әr
need help with number 2 1 For the two vectors in the x-y plane, a) Calculate the sum of the vectors (R) by first calculating Rx and Ry (the scalar sums of the x and b) c) y components, respectively) and then writing the vector result R in ijk summation format. Draw the graphical representation of the summation of the two vectors, this should include x-y reference axes, the two original vectors, and the resultant R. Calculate the magnitude of...
4. Consider the three displacement vectors shown in the figure: Vector A has a magnitude of 750 km and a direction that makes an angle 290% to the left of the positive y-axis vector B has a magnitude of 5.80 km and a direction that makes an angle of α =35.0° above the positive x-axis, and vector C has a magnitude of 3.10 km and a direction that makes an angle = 67.0 below the negative x-axis Determine the magnitude...