Two marks exercise problems II — task. Mathematics State Board, Class 10.

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1. If

A = (\begin{array}{l} 5 & 4 & 3 \\ 1 & - 7 & 9 \\ 3 & 8 & 2 \end{array})

, then find the transpose of \(A\).

\(A^T =\)

(\begin{array}{l} i & i & i \\ i & i & i \\ i & i & i \end{array})

2. If

A = (\begin{array}{l} \sqrt{7} & - 3 \\ - \sqrt{5} & 2 \\ \sqrt{3} & - 5 \end{array})

, then find the transpose of \(-A\).

\((-A)^T =\)

(\begin{array}{l} - \sqrt{i} & \sqrt{i} & - \sqrt{i} \\ i & i & i \end{array})

3. If

A = (\begin{array}{l} 5 & 2 & 2 \\ - \sqrt{17} & 0.7 & \frac{5}{2} \\ 8 & 3 & 1 \end{array})

, then verify \((A^T)^T = A\).

\(A^T =\)

(\begin{array}{l} i & - \sqrt{i} & i \\ i & i & i \\ i & \frac{i}{i} & i \end{array})

\((A^T)^T =\)

(\begin{array}{l} i & i & i \\ - \sqrt{i} & i & \frac{i}{i} \\ i & i & i \end{array})

\(=\)

Hence verified.

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4. Two marks exercise problems II