Prove that the determinants are equal

• Mar 20th 2009, 03:47 AM
sunitaparija
Prove that the determinants are equal
b+c-a a a a b c
b c+a-b b = b c a
c c a+b-c c a b
• Mar 20th 2009, 04:24 AM
mr fantastic
Quote:

Originally Posted by sunitaparija
b+c-a a a a b c
b c+a-b b = b c a
c c a+b-c c a b

The brute force approach:

Calculate $\left| \begin{array}{ccc}
b + c - a & a & a \\
b & c + a - b & b \\
c & c & a + b - c \end{array} \right|$
.

Calculate $\left| \begin{array}{ccc}
a & b & c \\
b & c & a \\
c & a & b \end{array} \right|$
.

Alternatively, you could do row operations on $\left| \begin{array}{ccc}
a & b & c \\
b & c & a \\
c & a & b \end{array} \right|$
.
• Mar 20th 2009, 04:27 AM
sunitaparija
The Determinant sum has to be proved without expanding.