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NCERT Class 12 · Ch 4 Exercise 4.5 · Q3

NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.5 Question 3

Examine consistency. Use the matrix method for AX=B, where A = \(\left[\begin{matrix}1 & 3\\2 & 6\end{matrix}\right]\), B = \(\left[\begin{matrix}5\\8\end{matrix}\right]\), X=\(\left[\begin{matrix}x\\y\end{matrix}\right]\).

💡 Concept Hints

  1. Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
  2. For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.

✅ Step-by-Step Solution

Final Answer: Inconsistent; no solution.
  1. For a 2×2 matrix use det A=a₁₁a₂₂−a₁₂a₂₁.
  2. \(6\) − \(6\) = \(0\).
  3. First check whether this determinant is zero.
  4. The determinant vanishes, so the matrix is singular and has no inverse.
  5. The coefficient rank is 1 and the augmented rank is 2.
  6. Unequal ranks establish inconsistency.

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