What the Determinant Means Worksheet with Answer Key

What's on the worksheet

1. The quadrilateral R has vertices P_1(1, 0), P_2(4, 0), P_3(3, 2) and P_4(1, 2), in counterclockwise order.
2. Vectors u and v in R² have S(u, v) = 6; nothing else about them is known.
3. For each map of the plane, write its matrix, give the factor by which it multiplies areas, and say whether it keeps orientation, reverses it, or…
4. For a number k, let A_k = \begin{bmatrix} k & 2 \\ 3 & k - 5 \end{bmatrix}.
5. Let C = \begin{bmatrix} 3 & 1 & 0 \\ 0 & 2 & 1 \\ 1 & 0 & -1 \end{bmatrix}. The solid W is the tetrahedron with vertices O, (2, 0, 0), (0, 3, 0) and…
6. P Q K P' Q' K' O The figure shows the triangle PQK and its image P'Q'K' under a linear map T(x) = Ax, where P' is the image of P, Q' of Q and K' of K.
7. Olivia's laser cutter places a logo on a sheet of acrylic in two linear steps: