First slide

Introduction to Determinants

Question

If matrix A is given by $A = [\begin{array}{cc} 6 & 11 \\ 2 & 4 \end{array}]$ , then the determinant of A²⁰⁰⁵ _ 6A²⁰⁰⁴ is

Moderate

A

2²⁰⁰⁶
B

(-11) 2²⁰⁰⁵
C

- 2²⁰⁰⁵ . 7
D

(-9) 2²⁰⁰⁴

Solution

$\begin{array}{rcl} |A^{2005} - 6 A^{2004}| & = & | A |^{2004} | A - 6 I | \\ = & 2^{2004} |\begin{matrix} 0 & 11 \\ 2 & - 2 \end{matrix}| = (- 22) 2^{2004} = (- 11) (2)^{2005} \end{array}$

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