Five marks example problems III — task. Mathematics State Board, Class 10.

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1. If \(A =\)

(\begin{array}{l} 1 & - 1 & 2 \end{array})

, \(B =\)

(\begin{array}{l} 1 & - 1 \\ 2 & 1 \\ 1 & 3 \end{array})

and \(C =\)

(\begin{array}{l} 1 & 2 \\ 2 & - 1 \end{array})

, show that \((AB)C = A(BC)\).

2. If \(A =\)

(\begin{array}{l} 1 & 1 \\ - 1 & 3 \end{array})

, \(B =\)

(\begin{array}{l} 1 & 2 \\ - 4 & 2 \end{array})

, \(C =\)

(\begin{array}{l} - 7 & 6 \\ 3 & 2 \end{array})

, verify that \(A(B + C) = AB + AC\).

3. If \(A =\)

(\begin{array}{l} 1 & 2 & 1 \\ 2 & - 1 & 1 \end{array})

and \(B =\)

(\begin{array}{l} 2 & - 1 \\ - 1 & 4 \\ 0 & 2 \end{array})

, show that \((AB)^T = B^T A^T\).

Important!

This is a self-assessment task. Solve this question and assess the solution steps after completing the exercise.

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6. Five marks example problems III