Suppose that t : r3 → r2 is given by:
t(a b c) = (a b)
a. prove that t is a linear transformation.
b. find the matrix a such that t(x) = ax.

 The required answers are

(a) T is proved to be a linear transformation.

(b) The matrix A such that T(x) = Ax is

Step-by-step explanation:  We are given a linear transformation T : R³ → R² defined as follows :

We are to

(a) prove that T is a linear transformation

and

(b) find a matrix A such that T(x) = Ax.

(a) Let s, t are any real numbers and (a, b, c), (a', b', c') ∈ R³.

Then, we have

So, we get

Therefore, T is a linear transformation.

(b) We know that B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} is a standard basis for R³ and B' = {(1, 0), (0, 1)} is a standard basis for R².

So, we have

So, the matrix A such that T(x) = Ax will be given by

Thus,

(a) T is proved to be a linear transformation.

(b) The matrix A such that T(x) = Ax is  

the answers are in the images, i received 100% on this assignment. hope this !

after 1 year: 221 deer

step-by-step explanation:

30% of 170 is 51. 170+51=221