Grade 11 Linear Transformation Worksheet
This worksheet covers fundamental concepts of linear transformations including matrix representation, transformations in 2D, and properties of linear maps for Grade 11 students.
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Grade 11 Linear Transformation Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Which of the following is NOT a property of a linear transformation T: V -> W?
T(u + v) = T(u) + T(v)
T(cu) = cT(u)
T(0) = 0
T(uv) = T(u)T(v)
2. The matrix representation of a rotation by 90 degrees counter-clockwise around the origin in 2D is:
[[0, -1], [1, 0]]
[[0, 1], [-1, 0]]
[[1, 0], [0, 1]]
[[-1, 0], [0, -1]]
3. A linear transformation maps the zero vector to the vector.
4. The of a linear transformation is the set of all vectors v such that T(v) = 0.
5. Determine if the transformation T: R² → R² defined by T(x, y) = (x + y, x - y) is linear. Justify your answer.
6. Find the standard matrix for the linear transformation T: R² → R² that first reflects points through the y-axis and then dilates by a factor of 3.
7. The composition of two linear transformations is always a linear transformation.
True
False
8. A linear transformation must preserve the magnitude of vectors.
True
False
9. Plot the vector v = [1, 2] and its image under the linear transformation T(x) = [[2, 0], [0, 1]]x on the coordinate plane below.