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