<p>The ratio of the trace of matrix <i>B</i> to matrix <i>C</i> is (where <i>C</i> = (<i>A</i> ⋅ <i>B</i>))</p>
Step-by-Step Solution
Key Concept: The trace of a product matrix can be related to the traces of individual matrices and their transformations.
<p><strong>Step 1:</strong> Matrix <i>B</i> = [<i>C</i><sub>1</sub> <i>C</i><sub>2</sub> <i>C</i><sub>3</sub>] with columns from the previous question.</p><p><strong>Step 2:</strong> Calculate trace(<i>B</i>) = sum of diagonal elements of <i>B</i>.</p><p><strong>Step 3:</strong> Calculate <i>C</i> = <i>A</i> ⋅ <i>B</i> = [<i>AC</i><sub>1</sub> <i>AC</i><sub>2</sub> <i>AC</i><sub>3</sub>]</p><p><strong>Step 4:</strong> Calculate trace(<i>C</i>) = sum of diagonal elements of <i>C</i>.</p><p><strong>Step 5:</strong> Ratio = trace(<i>B</i>) / trace(<i>C</i>) = -9/5</p><p>∴ Answer is (a).</p>
Correct Answer: a