Question

Let T:R3→R3T:ℝ3→ℝ3 be a linear transformation such that T(1,0,0)=(2,1,3)T(1,0,0)=(2,1,3), T(0,1,0)=(−1,1,0)T(0,1,0)=(-1,1,0), and T(0,0,1)=(1,2,−2)T(0,0,1)=(1,2,-2). Evaluate T(1,0,1)T(1,0,1).

Answer 1

T(1,0,1) = (3, 3, 1).

Explanation:

To evaluate T(1,0,1), we can use the linearity of the transformation. Since T is a linear transformation, we have:

T(1,0,1) = T(1,0,0) + T(0,0,1)

We know the values of T(1,0,0) and T(0,0,1) from the given information:

T(1,0,0) = (2,1,3)

T(0,0,1) = (1,2,-2)

Therefore,

T(1,0,1) = (2,1,3) + (1,2,-2)

= (2 + 1, 1 + 2, 3 - 2)

= (3, 3, 1)

So, T(1,0,1) = (3, 3, 1).