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Back to Exercise: Work with 2x2 matrices as transformations

Exercises: Work with 2x2 Matrices as Transformations

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Grade 9·20 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-12
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A

Recall / Warm-Up

1

To understand what a 2×22 \times 2 matrix AA does to the entire plane, you need to track only two special vectors. Which two?

2

The unit square has vertices at (0,0)(0,0), (1,0)(1,0), (0,1)(0,1), and (1,1)(1,1). Under any 2×22 \times 2 transformation AA, where does the origin (0,0)(0,0) always go?

3

The 2×22 \times 2 identity matrix II is applied to the unit square. What is the area of the image?

B

Fluency Practice

1

For A=[3102]A = \begin{bmatrix}3 & 1\\0 & 2\end{bmatrix}, where does e2=[01]\mathbf{e}_2 = \begin{bmatrix}0\\1\end{bmatrix} map under AA?

2

Matrix A=[2003]A = \begin{bmatrix}2 & 0\\0 & 3\end{bmatrix}. Where does the vertex (1,1)(1,1) of the unit square map?

3

The unit square has area 1. Matrix A=[3102]A = \begin{bmatrix}3 & 1\\0 & 2\end{bmatrix} is applied. What is the area of the image parallelogram?

4

A region of area 4 is transformed by matrix AA with det⁡(A)=−3\det(A) = -3. What is the area of the image?

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