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TS EAMCET · Maths · Matrices

Consider the simultaneous linear equations \(\mathrm{AX}=\mathrm{B}\) and \(\mathrm{AY}=\mathrm{Q}\). If \(\mathrm{A}\) is an invertible matrix and \(\mathrm{B}\) is the unique solution of \(\mathrm{AY}=\mathrm{Q}\), then the solution of \(\mathrm{AX}=\mathrm{B}\) is

  1. A \(A^{-1}(B+Q)\)
  2. B \(\left(A^{-1}\right)^2 B\)
  3. C \(\mathrm{A}^{-1} \mathrm{BQ}\)
  4. D \(\left(A^{-1}\right)^2 Q\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(A^{-1}\right)^2 Q\)

Step-by-step Solution

Detailed explanation

Given linear equations \(\mathrm{AX}=\mathrm{B}\) and \(\mathrm{AY}=\mathrm{Q}\). Here, \(\mathrm{AY}=\mathrm{Q}\) has unique solution \(\mathrm{B}\). Then, \(\mathrm{AB}=\mathrm{Q}\) Take, \(\mathrm{AY}=\mathrm{B}\) Multiply both side by A.…