Question

Find the transition matrix from B to B'. B = {(-1,2), (3, 4)), B' = {(1, 0), (0, 1)} STEP 1: Begin by forming the following matrix -1 2 0 [B":8] = 4 0 STEP 2: Determine the transition matrix. -2/5 3/10 1/10 Need Help? Read It Talk to a Tutor

Answer 1

Answer:  The required matrix is

$T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .$

Step-by-step explanation:  We are given to find the transition matrix from the bases B to B' as given below :

B = {(-1,2), (3, 4)) and B' = {(1, 0), (0, 1)}.

Let us consider two real numbers a, b such that

$(-1,2)=a(1,0)+b(0,1)\\\\\Rightarrow (-1,2)=(a,b)\\\\\Rightarrow a=-1,b=2.$

Again, let us consider reals c and d such that

$(3,4)=c(1,0)+d(0,1)\\\\\Rightarrow (3,4)=(c,d)\\\\\Rightarrow c=3,d=4.$

Therefore, the transition matrix is given by

$T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .$

Thus, the required matrix is

$T=\left[\begin{array}{ccc}-1&3\\2&4\end{array}\right] .$