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3 and 4 .Determinants and Matrices
normal
If $\left| {\begin{array}{*{20}{c}}{a\, + \,1}&{a\, + \,2}&{a\, + \,p}\\{a\, + \,2}&{a\, +\,3}&{a\, + \,q}\\{a\, + \,3}&{a\, + \,4}&{a\, + \,r}\end{array}} \right|$ $= 0$ , then $p, q, r$ are in :
A
$AP$
B
$GP$
C
$HP$
D
none
Solution
Use $R_2 \rightarrow R_2 – R_1 \, \& \, R_3 \rightarrow R_3 – R_2 \, \& $ then $c_1 \rightarrow c_1 – c_2$ to get $\left| {\,\begin{array}{*{20}{c}}{ – 1} & {a +2}&{a + p}\\0 &1&{q – p}\\0&1&{r – q}\end{array}\,} \right|$ open by $c_1$ to get $p + r = 2q$
Standard 12
Mathematics
