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Mathematik-Online problems:

Problem 60: Calculation of Determinants

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given the matrices

$\displaystyle A=\left(\begin{array}{rrrrr} 2 & 0 & 0 & -3 & 0 \\ 1 & 4 & 0 & 1... ... b \\ b & \cdots & b & b & a \\ \end{array}\right)\in\mathbb{R}^{n\times n}. $


a)
Find $ {\mathrm{det}}(A)$.
b)
Proof: $ {\mathrm{det}}(B)=\left[a+(n-1)b\right]\,(a-b)^{n-1}$.

(Authors: Strauss/Kimmerle/Roggenkamp/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004