Let T be the rotation about the origin of angle followed by thereflection in the x-axis. Find T[1 0].(i)

The transformation T consists of two parts: a rotation about the origin and a reflection in the x-axis.

Step 1: Rotation about the origin The rotation matrix for an angle θ is given by: [[cos(θ), -sin(θ)], [sin(θ), cos(θ)]]

However, the angle is not given in the question. Let's assume the angle is θ.

Step 2: Reflection in the x-axis The reflection in the x-axis can be represented by the matrix: [[1, 0], [0, -1]]

Step 3: Apply the transformations to the vector [1 0] First, we apply the rotation: [cos(θ)*1 - sin(θ)*0, sin(θ)*1 + cos(θ)*0] = [cos(θ), sin(θ)]

Then, we apply the reflection: [1cos(θ) + 0sin(θ), 0cos(θ) - 1sin(θ)] = [cos(θ), -sin(θ)]

So, T[1 0] = [cos(θ), -sin(θ)].

Please note that the actual result may vary depending on the specific angle of rotation θ.