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Question

If pbcaqcabr=0, find the value of pp-a+qq-b+rr-c, pa, qb, rc.

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Solution

Let =pbcaqcabr.
Now,
=pbcaqcabr =pbc0q-bc-rabr Applying R2R2-R3 =prq-b-bc-r+abc-r-cq-b Expanding along first column =prq-b+pbr-c-abr-c-acq-b =pr-acq-b+bp-ar-cSince, =0. pr-acq-b+bp-ar-c=0pr-acp-ar-c+bq-b=0pr-ar+ar-acp-ar-c+bq-b=0rp-a+ar-cp-ar-c+bq-b=0rr-c+ap-a+bq-b=0pp-a+qq-b+rr-c=pp-a+qq-b-ap-a-bq-bpp-a+qq-b+rr-c=p-ap-a+q-bq-bpp-a+qq-b+rr-c=2Hence, the value of pp-a+qq-b+rr-c is 2.

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