(a) find the transition matrix from B to&nbsp;B′,&nbsp;(b) find the transition matrix from&nbsp;B′&nbsp;to B,&nbsp;(c) verify that the two transition matrices are inverses of each other(d) Solve the coordinate matrix&nbsp;[x]B, given the coordinate matrix&nbsp;[x]B.&nbsp;B={(1,3),(−2,−2)},B‘={(−12,0),(−4,4)}[x]B′=[−13]

Question

(a) find the transition matrix from B to&amp;nbsp;B′,&amp;nbsp;(b) find the transition matrix from&amp;nbsp;B′&amp;nbsp;to B,&amp;nbsp;(c) verify that the two transition matrices are inverses of each other(d) Solve the coordinate matrix&amp;nbsp;[x]B, given the coordinate matrix&amp;nbsp;[x]B.&amp;nbsp;B={(1,3),(−2,−2)},B‘={(−12,0),(−4,4)}[x]B′=[−13]

Ancessitere · Accepted Answer

(a) Start by creating the augmented matrix (B’B):&amp;nbsp;(B‘B)=(−12−41−2043−2)&amp;nbsp;Using Gauss-Jordan elimination we obtain the above in the form&amp;nbsp;(IP−1)&amp;nbsp;(IP−1)=(10−1/31/3013/4−1/2)&amp;nbsp;Then, the transition matrix form B to B’ is:&amp;nbsp;P−1=(−1/31/33/4−1/2)

Jeffrey Parrish · Accepted Answer

(b) First form the matrix (BB’)  (BB‘)=(1−2−12−43−204)  By Gauss-lordan process we wrotte:  (IP)=(10640194)  The transition matrix from B’ to B is then:  (P)=(6494)

user_27qwe · Accepted Answer

(c) Calculating P−1P and PP−1 we obtain:  P−1P=(−1/31/33/4−1/2)(6494)=(1001)=I  P−1=(6494)(−1/31/33/4−1/2)=(1001)  Then P−1 the inverse of P.  (d) We have in the basis B  (x)B=P(x)B‘=(6494)(−13)=(63)

(a) find the transition matrix from B to B', (b) find the transitio

Answered question

Answer & Explanation

New Questions in Linear algebra