Question

Let B = {(1,0), (0, 1)} and B = {(0,1), (1, 1) } be two V=1R². Moreover, het cuib - [1 -2] and the for T relative to 3 be Maitrise 2 2 from B to B Ces Find The treinsition matrix 6. Use the matrices P and A to find [v] and [Ta] (c) Find A (the matrix for ī relative to B') Find [T(4) In and

Answer 1

Given that the Soin let B = B! {(1,0), (0,1)] {10,1)))} A= 2 & [U5L-277 B 22 (62)e] the transition matrix P from B to B P= [(b)), where bi and bi are Elements in al (0,1) olise +1 (0,0) (1.1) . 1 (1,0) +1:(0,1)

[ue] = (0,1 = 0.(1,0)+1 (0,1) = ((0.1))o - 10] (1,1) 1(1,0.)+ 110,1) = {(1,1)) = 2 P=[9) Then the transition matrix (from B to B is P= 18:] Pavle " (1-2) 18:).C-1) = (-3) (-3) (Ve)= [•]-110] - (3) (4-33-1-1] Tlu] - -616] T(U) ( T: = -2 TC) = (22][-] 6 (2] 1210] & 6 2 B

O we already found Hecet te freu)(47 ū= (-2) and Erculo = ? U= a frows] = 8' (Tw] adip (det) (det p) = (0-1) :-) pu't , where P=209) adio = 14 3 6+2 8 -6 p=46-) - fd] [Trondi = 46) 41 - T(U) -670 [:)] B B [(nad) pusy of hom hout Cov) Another = Ercus 8 [9]-«[?] -607 ( [T(v)= (*); 1860) 8(1)–61) 6 مل [T(m)] = 8[] - [1] 1 8 Frosol (-8