Q19 of 45 Page 1

Using properties of determinants, prove the following:

Given


Performing the operation C1→ C1 – C3 and C2→ C2 – C3, we get



Performing the operation C1→ C1 – aC3,



Expanding along R1, we get


= ac – b (-c – a – ac)


= ac + bc + ba + bac


= ab + bc + ca + abc


= RHS


Hence proved.


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