Matrices & Determinants
Determinants
Grade Class 12
Question:
If α, β ≠ 0, and f(n) = α^n + β^n and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
(1) αβ
(2) <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>α</mi><mi>β</mi></mrow></mfrac></math>
(3) 1
(4) -1
Step-by-Step Solution
Key Concept: The determinant can be expressed as the product of two matrices, each being a Vandermonde-like matrix involving \alpha and \beta.
The given determinant can be written as the product of two matrices: <br> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
Correct Answer: (3)