LA2.1.15

From Exampleproblems

Jump to: navigation, search

Without expanding the determinant prove that \begin{vmatrix} 1 & bc & b+c \\ a & ca & c+a \\ 1 & ab & a+b \end{vmatrix}=\begin{vmatrix} 1 & a & a^2 \\1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}\,

LHS=\begin{vmatrix} 1 & bc & b+c \\ a & ca & c+a \\ 1 & ab & a+b \end{vmatrix}\,

By C-3-(a+b+c)C_1\, we get

\begin{vmatrix} 1 & bc & -a \\ 1 & ca & -b \\ 1 & ab & -c \end{vmatrix}\,

By aR_1,bR_2,cR_3\,

\frac{1}{abc} \begin{vmatrix} a & abc & -a^2 \\ b & abc & -b^2 \\ c & abc & -c^2 \end{vmatrix}\,

\frac{abc}{abc}\begin{vmatrix} a & 1 & -a^2 \\ b & 1 & -b^2 \\ c & 1 & -c^2 \end{vmatrix}\,

\begin{vmatrix} 1 & a & -a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}\,=RHS


Main Page:Linear Algebra

Retrieved from "http://www.exampleproblems.com/wiki/index.php/LA2.1.15"
Argan Oil
Natural Skin Care
Organic Skin Care
visitor stats