LA2.1.13

From Example Problems
Jump to: navigation, search

Show that {\begin{vmatrix}a&a+b&a+b+c\\2a3a+2b&4a+3b+2c\\3a&6a+3b&10a+6b+3c\end{vmatrix}}=a^{3}\,

Applying R_{2}-2R_{1},R_{3}-3R_{1}\, to the given,we get

{\begin{vmatrix}a&a+b&a+b+c\\2a3a+2b&4a+3b+2c\\3a&6a+3b&10a+6b+3c\end{vmatrix}}={\begin{vmatrix}a&a+b&a+b+c\\0&a&2a+b\\0&3a&7a+3b\end{vmatrix}}\,

a[a(7a+3b)-3a(2a+b)]=a^{3}\,=RHS


Main Page:Linear Algebra