Determinants ( help needed )

If \begin{vmatrix} p & b & c\\ a & q & c\\ a& b & r \end{vmatrix}=0

find the value of pp-a + qq-b + rr-c
where a≠p. b≠q , and c≠r

ans---- 2

4 Answers

3
msp ·

mmm seems easy when u use this p=b=c=0

1
Manmay kumar Mohanty ·

any one ???

11
SANDIPAN CHAKRABORTY ·

\begin{vmatrix} p &b &c\\ a &q &c \\ a &b &r \end{vmatrix}

R2-------------->R2 - R3

\begin{vmatrix} p &b &c\\ 0 &q-b &c-r \\ a &b &r \end{vmatrix}

R3-------------->R3 - R1

\begin{vmatrix} p &b &c\\ 0 &q-b &c-r \\ a-p &0 &r-c \end{vmatrix}

Taking (p-a)(q-b)(r-c)common from C1, C2, C3 respectively we get....

(p-a)(q-b)(r-c)\begin{vmatrix} \frac{p}{p-a} &\frac{b}{q-b} &\frac{c}{r-c}\\ 0 &1 &-1 \\ -1 &0 &1 \end{vmatrix}

expanding along R1

pp - a + bq - b + cr - c = 0

or

pp - a + b + q - qq - b + c + r - rr - c = 0

or

pp - a + qq - b - 1 + rr - c - 1 = 0

or..

pp - a + qq - b + rr - c = 2

answer....

1
Manmay kumar Mohanty ·

simply Gr8 SANDIPAN [1][1]

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