a. The linear transformation T_1: R^2 \rightarrow R^2 is given by:

T_1(x, y) = (2 x + 5 y, 8 x + 21 y) .

FindT_1^{-1}(x, y) .

T_1^{-1}(x, y) = ( x + y, x + y)

b. The linear transformationT_2: R^3 \rightarrow R^3 is given by:

T_2(x, y, z) = (x + 1 z, 2 x + y, 2 y + z) .

FindT_2^{-1}(x, y, z) .

T_2^{-1}(x, y, z) = ( x + y + z, x + y + z, x + y + z)

c. UsingT_1 from part a, it is given that:

T_1(x, y) = (3, -4)

Find x and y.

x = y =

d. UsingT_2 from part b, it is given that:

T_2(x, y, z) = (5, -5, 1)

Find x, y, and z.

x = y = z =

Find

b. The linear transformation

Find

c. Using

Find x and y.

d. Using

Find x, y, and z.

You can earn partial credit on this problem.