Matrix transformations · Short practice

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Recall

Linear transformations and invariant lines — objective 1

Maths4U Original · Short practice

\(A=\left[\begin{matrix}12 & 13\\0 & 15\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the area scale factor of A.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Linear transformations and invariant lines — objective 1

Maths4U Original · Short practice

\(A=\left[\begin{matrix}13 & 14\\0 & 16\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the area scale factor of A.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Method

Linear transformations and invariant lines — objective 2

Maths4U Original · Short practice

\(A=\left[\begin{matrix}13 & 14\\0 & 16\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the nonzero finite slope of an invariant line of A through the origin.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Linear transformations and invariant lines — objective 2

Maths4U Original · Short practice

\(A=\left[\begin{matrix}14 & 15\\0 & 17\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the nonzero finite slope of an invariant line of A through the origin.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Apply

Linear transformations and invariant lines — objective 3

Maths4U Original · Short practice

\(A=\left[\begin{matrix}14 & 15\\0 & 17\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the (1,1) entry of AB.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Linear transformations and invariant lines — objective 3

Maths4U Original · Short practice

\(A=\left[\begin{matrix}15 & 16\\0 & 18\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the (1,1) entry of AB.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Check understanding

Linear transformations and invariant lines — objective 4

Maths4U Original · Short practice

\(A=\left[\begin{matrix}15 & 16\\0 & 18\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the (2,1) entry of AB.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Fresh review variant

Linear transformations and invariant lines — objective 4

Maths4U Original · Short practice

\(A=\left[\begin{matrix}16 & 17\\0 & 19\end{matrix}\right],\ B=\left[\begin{matrix}1 & 0\\1 & 1\end{matrix}\right]\). Use column vectors; AB means B acts first.

Find the (2,1) entry of AB.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

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