MathematicsIf k>I, and the determinant of the matrix A2 , where A = kkaa0aka00k, is k2 then a =

If k>I, and the determinant of the matrix A² , where A = $[\begin{matrix} k & k a & a \\ 0 & a & k a \\ 0 & 0 & k \end{matrix}]$ , is k²then $|\begin{matrix} a \end{matrix}| =$

A
$\frac{1}{k^{2}}$
B
k
C
$k^{2}$
D
$\frac{1}{k}$

Solution:

$|A| = |\begin{matrix} k & k a & a \\ 0 & a & k a \\ 0 & 0 & k \end{matrix}| = k^{2} a {|A|}^{2} = k^{4} a^{2} = k^{2} \Rightarrow a^{2} = \frac{1}{k^{2}} ∴ |a| = \frac{1}{k}$

Related content

Area of Square

Area of Isosceles Triangle

Pythagoras Theorem

Triangle Formulae

Perimeter of Triangle Formula

Area Formulae

Volume of Cone Formula

Matrices and Determinants_mathematics

Critical Points Solved Examples

Type of relations_mathematics