Determine whether the given matrix is orthogonal. If it is, find its inverse. cos sin cos...
| sin(0) Use the identity matrix to find the inverse of A = l-cos(0) cos(0) sin(0)
e-30 sin() -1 backward substitution method 4. Given A = sin(t) cos(t) tanto find the following 0 a. Matrix of minors (2pts) b. Matrix of cofactors (2pts) c. Adjoint matrix (2pts) d. Determinant of A (2pts) Inverse of A using the Adjoint matrix. (2pts) e. 1 v T.
Determine whether the matrix is orthogonal. P= 1 3 2 3 2 | ابداع | الا تہ نما wwNWIN Find ppt 10 0 10 It 10 0 1 Is the matrix P is orthogonal? Pis orthogonal. O P is not orthogonal. 3 Let Pi P2 and p3 If the matrix Pis orthogonal, show that the column vectors of the matrix form an orthonormal Find Pip2 PiP2 Find Pip3 PIP3 Find p2.ps P2 P3 - Find pull pall Find ||p2|| lipall...
4. We saw in class that if A is an orthogonal matrix, then ||AX|| = ||X||. One matrix for which we know this is true is the rotation matrix, A = [cos – sin 0] sin cos a. (2 pts) Show that A is an orthogonal matrix. b. (2 pts) Since A is an orthogonal matrix, A-1 = AT. Show that AT can be written as cos 0 – sino w does the angle o relate to the angle ?...
Matrix operations 22. Suppose you are given a matrix of the form cos(() - sin(0) R(0) = sin() cos(0) Consider now the unit vector v = [1,0)" in a two dimensional plane. Compute R(O)v. Repeat your computations this time using w = [0, 1]". What do you observe? Try thinking in terms of pictures, look at the pair of vectors before and after the action of R(O). 23. You may have recognised the two vectors in the previous question to...
10) Determine whether the matrix operator is invertible, if so, find its inverse. a)T(x, y) = (3x + 4y, 5x + 7y) b)T(x1, X2 X3) = (x; + 2x2 + 3x3, xz – X3, X; +3x2 + 2x3)
Determine whether or not the given function is one-to-one and if so, find the inverse. If f(x) = (4x + 2)* has an inverse, give the domain of f-1. a) Of c) = (2 - 4x)1/4; domain: 2) 2 - 1/4 b) O f-1(2) = domain: (0,0) 4 c) Not one-to-one d) Of () 1/4 - 2 -; domain: (-0,0) 4 e) Of (2) = 2-1/4 -; domain: 4 (1:0) Question 4 Determine whether or not the given function is...
2. Inverse of a square matrix: Determine the inverse matrix [A™'] of the given square matrix [A] using the Gauss-Jordan Elimination Method (GEM), and verify that [A-!] [A] = I where I is the identity matrix. A = [ 1 4 -27 0 -3 -2 | -3 4 1
Find the inverse, if it exists, of the given matrix 1 0 0 OA. 0 1 1 0 0 1 1 0 0 2-1 1 Find the inverse, if it exists, of the given matrix. 5 12 5 2 A. 12 5 5 -12 -2 5 -5 2 12 -5 -5-12 -25 OB. O c. O D. Determine whether the two matrices are inverses of each other by computing their product. 9 4-22 2 -45 O No O Yes
5. Determine whether or not matrix A shown below is orthogonal and justify your answer. 0 -21 A = 10 INOMI- 1 0 0 1