Matrices & Determinants
Determinants
Grade 12
Question:
<p>If \(p\sqrt{2} + 3\sqrt{4} + q\sqrt{3} + r\sqrt{2} + s\sqrt{1} + t = \sqrt{2} + 1\) and \(\begin{vmatrix} 2+3\sqrt{4} & \sqrt{4}-1 & \sqrt{4}+3 \\ \sqrt{2}+1 & 2-\sqrt{4} & \sqrt{4}-3 \\ \sqrt{2}-3 & \sqrt{4}+4 & 3\sqrt{4} \end{vmatrix}\), then \(t\) is equal to</p>
<p>(a) \(7\)</p>
<p>(b) \(14\)</p>
<p>(c) \(21\)</p>
<p>(d) \(28\)</p>
Step-by-Step Solution
Key Concept: Relate a determinant value to a linear combination involving radicals to isolate and find $t$.
<p>Evaluate the given determinant and use the relationship between the determinant value and the linear combination to solve for $t$.</p>
Correct Answer: D