Properties of Matrices (Edexcel A-Level Further Mathematics): Quizzes

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Matrix Dimensions
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A matrix has 3 rows and 2 columns. What are its dimensions?

3×23 \times 2

What is the 3D identity matrix?

(100010001)\begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}

What does the determinant of a 3D transformation matrix represent?

Scale factor of volume change

A shape with volume 10 is transformed by a matrix with determinant 15-15. What is the new volume?

150150

What does a negative determinant indicate about a transformation?

Orientation has changed

What is the plane z=0z = 0 also called?

xx-yy plane

What is the reflection matrix for the z=0z = 0 plane?

(100010001)\begin{pmatrix}1&0&0\\0&1&0\\0&0&-1\end{pmatrix}

What is the reflection matrix for the x=0x = 0 plane?

(100010001)\begin{pmatrix}-1&0&0\\0&1&0\\0&0&1\end{pmatrix}

In a reflection, what happens to the unaffected coordinates?

They remain the same

Which coordinate remains unchanged during rotation about the zz-axis?

zz-coordinate

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