Give a linear transformation T R3 rightarrow R3 defined as T

Give a linear transformation T: R^3 rightarrow R^3 defined as T (x y z) = (x + y + z x + y z) Find the standard matrix A for T and Determinant of A. Give a 3 by 3 matrix A and assume that det(-2A) = 64. Find det (2/3 A^t)

Solution

We have,

Det(A)=Det(A^t)

Det(pA)=p Det(A)

Given,

Det(-2A)=64

So, -2 Det(A)=64

Then, Det(A)= -32

As, Det(A) = Det(A^t)

Det(A^t)= -32

Therefore ,

Det((2/3)A^t)= (2/3)Det(A^t)

= (2/3)*(-32)

= (-64/3)