Let Eequals={Bold e 1e1, Bold e 2e2, Bold e 3e3} be the standard basis for set of real numbers Rℝ3, Bequals={Bold b 1b1, Bold b 2b2, Bold b 3b3} be a basis for a vector space V, and T : set of real numbers Rℝ3 right arrow→ V be a linear transformation with the property that Upper T (x 1 comma x 2 comma x 3 )Tx1, x2, x3equals=(x 2 minus x 3 )x2−x3Bold b 1b1plus (x 1 plus x 3 )+x1+x3Bold b 2b2plus (x 2 minus x 1 )+x2−x1Bold b 3b3.

a. Find the change-of-coordinates matrix from Upper B to Upper A.
b. Find left bracket Bold x right bracket Subscript Upper A for Bold x equals Bold b 1 minus 4 Bold b 2 plus 4 Bold b 3.