miet В.С be bases of R2 such that PO--B-l, 22]and B-{(1).(1)) Find C. 1(2 miet В.С be bases of R2 such that PO--B-l, 22]and B-{(1).(1)) Find C. 1(2
Let B = {(1 2),(3 5)} and B'= {(1-1),(1-2)} be two bases of R2. Also, let TB: R2→R2 be a linear operator on B described as TB(x,y) = (x+2y,x+y). Find TB'.
2) Let B = {(1, 3, 4), (2,-5,2), (-4,2-6)) and B/-(( 1, 2,-2), (4, 1,-4), (-2, 5, 8)) be 5 ordered bases of R2. Let x = | 8 | in the standard basis of R2. a) Use a matrix and x to find L18 ]B. b) Use a matrix and [X]B to find [x)B/. c) Use a matrix and [X]B/ to find x in the standard basis of R2, d) Draw a diagram of the steps a), b), and...
Let L : R2 → R3 be a linear transformation such that L 1 1 = 1 2 3 and L 1 2 = 2 1 3 . Find L 2 1 Find the standard matrix representing L. Find the dimensions of the kernel and the range of L and their bases. 12. Let L : R² + RP be a linear transformation such that L | (3) - -(5)-(1) Find I (*) Find the standard matrix representing L. Find...
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2
Question 2 (10 marks) Consider vectors b) (a) Show that B {bi, b2} and Ć = {ci. C2} are bases for R2 (b) Find the B-coordinates of x- (c) Find the change of coordinates matrix Pc-s from B to C and use it to find [x (d) Find the C-coordinates of y - (e) Find the change of coordinates matrix Psc from C to B and use it to find yg Question 2 (10 marks) Consider vectors b) (a) Show...
Let B = {b1,b2} and C= {(1,62} be bases for R2. Find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B. - 1 b = b2 = C1 = C = 4 -3 Find the change-of-coordinates matrix from B to C. P = CB (Simplify your answers.) Find the change-of-coordinates matrix from C to B. P B-C [8: (Simplify your answers.)
Given bases B = {(2,-3).(5,4)} and B' = {(1,0),(0, 1)) for R2 and coordinate matrix [3] * [8] + [6] find the following two things. The transition matrix from B to B' The coordinate matrix x[*],
AB matrix, linear operator R2 into R3 find the standard fro 11) For the linear operator L(x1, 22, ^1 + 22 AB matrix, linear operator R2 into R3 find the standard fro 11) For the linear operator L(x1, 22, ^1 + 22
(13) B = = {{]] • ]} and c = {{=} (1) are both bases for R2. (a) (5 points) Find the matrices P. and P CAB вес (b) (5 points) What is [7} if (c = [-] ? And what is v in standard coordinates? (.) (5 points) What is [v]e if [W]s = [2] ? And what is V in standard coordinates?
2) For a spherical charge distribution in the air: po (02 – r2), when r <a p. when r>a lo, (a) Find E and for r>a (b) Find E and for r<a (c) Find the total charge (d) Show that E is maximum when r=0.7454a