Question

a b c
-a b c
-a -b c
Evaluate​

Answer 1

Answer:

-a-bc

Step-by-step explanation:

abc-abc-a-bc

0-a-bc

Answer 2

Step-by-step explanation:

Given:

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

To find: Evaluate the determinant.

Solution:

Take a,b and c common from C1,C2 and C3 respectively

$=abc\left|\begin{array}{ccc}1&1&1\\-1&1&1\\-1&-1&1\end{array}\right|$

Perform row operation

$R_3->R_3+R_1$

$R_2->R_2-R_1$

$=abc\left|\begin{array}{ccc}1&1&1\\-2&0&0\\0&0&2\end{array}\right|$

Now expand the determinant along R1

$=abc[1(0)-1(-4)+1(0)]$

$=abc[4]$

$=4abc$

Final answer:

$\bold{\left|\begin{array}{ccc}a&b&c\\-a&b&c\\-a&-b&c\end{array}\right|=4abc}$

Hope it helps you.

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