Question

Assume that t is a linear transformation. Find the standard matrix of t. t: R² → R². First, it rotates points through -7pi/6 radians, and then reflects them.

Answer 1

To find the standard matrix of the given linear transformation t, we determine the rotation matrix for -7π/6 radians, the reflection matrix, and then multiply these matrices.

Step-by-step explanation:

To find the standard matrix of a linear transformation t that first rotates points through -7π/6 radians and then reflects them, we first need to find the rotation matrix, followed by the reflection matrix, and finally multiply the two matrices to obtain the standard matrix of t.

For rotation by an angle θ in R², the rotation matrix R(θ) is:

• R(θ) = [cos(θ) -sin(θ); sin(θ) cos(θ)]

For a reflection across the x-axis, the reflection matrix M is:

• M = [1 0; 0 -1]

Substituting θ = -7π/6 into R(θ) and then multiplying by M gives us:

1. Compute the rotation matrix R(-7π/6).
2. Compute the reflection matrix M.
3. Multiply R(-7π/6) by M to find the standard matrix for t.