AP EAMCET · Maths · Determinants
If \(A\) and \(B\) are the two real values of \(k\) for which the system of equations \(x+2 y+z=1\), \(x+3 y+4 z=k \cdot x+5 y+10 z=k^2\) is consistent, then \(A+B=\)
- A 3
- B 4
- C 5
- D 7
Answer & Solution
Correct Answer
(A) 3
Step-by-step Solution
Detailed explanation
Given system of equation is, \[ \begin{aligned} & x+2 y+z=1 \\ & x+5 y+10 z=k^2 \\ \therefore & \quad D=\left|\begin{array}{lll} 1 & 2 & 1 \\ 1 & 3 & 4 \\ 1 & 5 & 10 \end{array}\right| \\ = & 1(30-20)-2(10-4)+1(5-3)=10-12+2=0 \end{aligned} \] Since, \(\quad D=0\) \(\therefore\)…
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