Determinants · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Three-by-three matrices — objective 1

Maths4U Original · Short practice

\(A=\left[\begin{matrix}11 & 1 & 0\\0 & 12 & 1\\1 & 0 & 13\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}145\\171\\207\end{matrix}\right]\).

Find det 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

Three-by-three matrices — objective 1

Maths4U Original · Short practice

\(A=\left[\begin{matrix}12 & 1 & 0\\0 & 13 & 1\\1 & 0 & 14\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}170\\198\\237\end{matrix}\right]\).

Find det A.

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

Method

Three-by-three matrices — objective 2

Maths4U Original · Short practice

\(A=\left[\begin{matrix}12 & 1 & 0\\0 & 13 & 1\\1 & 0 & 14\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}170\\198\\237\end{matrix}\right]\).

Find the (1,1) entry of A inverse.

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

Fresh review variant

Three-by-three matrices — objective 2

Maths4U Original · Short practice

\(A=\left[\begin{matrix}13 & 1 & 0\\0 & 14 & 1\\1 & 0 & 15\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}197\\227\\269\end{matrix}\right]\).

Find the (1,1) entry of A inverse.

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

Apply

Three-by-three matrices — objective 3

Maths4U Original · Short practice

\(A=\left[\begin{matrix}13 & 1 & 0\\0 & 14 & 1\\1 & 0 & 15\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}197\\227\\269\end{matrix}\right]\).

Find the first coordinate of the solution of Av=b.

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

Fresh review variant

Three-by-three matrices — objective 3

Maths4U Original · Short practice

\(A=\left[\begin{matrix}14 & 1 & 0\\0 & 15 & 1\\1 & 0 & 16\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}226\\258\\303\end{matrix}\right]\).

Find the first coordinate of the solution of Av=b.

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

Check understanding

Three-by-three matrices — objective 4

Maths4U Original · Short practice

\(A=\left[\begin{matrix}14 & 1 & 0\\0 & 15 & 1\\1 & 0 & 16\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}226\\258\\303\end{matrix}\right]\).

Find trace(\(\displaystyle A^{2}\)).

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

Fresh review variant

Three-by-three matrices — objective 4

Maths4U Original · Short practice

\(A=\left[\begin{matrix}15 & 1 & 0\\0 & 16 & 1\\1 & 0 & 17\end{matrix}\right]\). For the system question use \(b=\left[\begin{matrix}257\\291\\339\end{matrix}\right]\).

Find trace(\(\displaystyle A^{2}\)).

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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