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3 and 4 .Determinants and Matrices
normal
$'a'$ ની . . . . કિમંત માટે સમીકરણો $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$ ; $ax + (a + 1)y + (a + 2)z = 0$ ; $x + y + z = 0$ ને શૂન્યતર ઉકેલ મળે.
A
$1$
B
$0$
C
$-1$
D
$2$
Solution
$\mathrm{d}_{1}=\mathrm{d}_{1}=\mathrm{d}_{3}=0 \Rightarrow \mathrm{D}_{1}=\mathrm{D}_{2}=\mathrm{D}_{3}=0$
$\mathrm{D}=\left|\begin{array}{ccc}{a^{3}} & {(a+1)^{3}} & {(a+2)^{3}} \\ {a} & {(a+1)} & {(a+2)} \\ {1} & {1} & {1}\end{array}\right|=0 \Rightarrow \mathrm{a}=-1$
Standard 12
Mathematics
