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TS EAMCET · Maths · Matrices

Let \(A=\left[\begin{array}{ccc}1 & -4 & 7 \\ 0 & 3 & -5 \\ -2 & 5 & -9\end{array}\right], B\left[\begin{array}{c}a \\ -b \\ -c\end{array}\right]\). If \(A\) and \([A: B]\) have same rank, then

  1. A \(2 a+b+c=0\)
  2. B \(a=\frac{b+c}{2}\)
  3. C \(b=\frac{a+c}{2}\)
  4. D \(c=\frac{a+b}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(a=\frac{b+c}{2}\)

Step-by-step Solution

Detailed explanation

\([A: B]=\left[\begin{array}{ccccc} 1 & -4 & 7 & : & a \\ 0 & 3 & -5 & : & -b \\ -2 & 5 & -9 & : & -c \end{array}\right]\) Applying \(R_3 \rightarrow R_3+2 R_1\)…