AP EAMCET · Maths · Matrices
If \(\frac{x^2+5 x+1}{(x+1)(x+2)(x+3)}=\frac{a}{x+1}+\frac{b}{(x+1)(x+2)}+\frac{c}{(x+1)(x+2)(x+3)}\) then the inverse of the matrix \(\left[\begin{array}{ll}a & b \\ c & 1\end{array}\right]\) is
- A \(\left[\begin{array}{cc}1 & 0 \\ -5 & 1\end{array}\right]\)
- B \(\left[\begin{array}{cc}-1 & 0 \\ 5 & -1\end{array}\right]\)
- C \(\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right]\)
- D \(\left[\begin{array}{ll}1 & 0 \\ 1 & 5\end{array}\right]\)
Answer & Solution
Correct Answer
(C) \(\left[\begin{array}{ll}1 & 0 \\ 5 & 1\end{array}\right]\)
Step-by-step Solution
Detailed explanation
\(x^2+5x+1 = a(x+2)(x+3) + b(x+3) + c\) \(x^2+5x+1 = ax^2 + (5a+b)x + (6a+3b+c)\) \(a = 1\) \(5 = 5a+b \Rightarrow 5 = 5(1)+b \Rightarrow b=0\) \(1 = 6a+3b+c \Rightarrow 1 = 6(1)+3(0)+c \Rightarrow c=-5\)…
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