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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
For two \(3\times3\) matrices \(A\) and \(B\) , let \(A+ B\, = 2B'\) and \(3A + 2B\, = I_3\), where \(B'\) is the transpose of \(B\) and \(I_3\) is \(3\times3\) identity matrix. Then
- A \(5A+ 10B\, = 2I_3\)
- B \(10A+ 5B\, = 3I_3\)
- C \(B+ 2A\, = I_3\)
- D \(3A+ 6B\, = 2I_3\)
Answer & Solution
Correct Answer
(B) \(10A+ 5B\, = 3I_3\)
Step-by-step Solution
Detailed explanation
\({A^T} + {B^T} = 2B\) \(\because \) \(\left[ {{{\left( {A + B} \right)}^T} = {{\left( {2B} \right)}^T}} \right]\) \( \Rightarrow B = \frac{{{A^T} + {B^T}}}{2} = A + \left( {\frac{{{A^T} + {B^T}}}{2}} \right) = 2{B^T}\) \(2A + {A^T} = 2{B^T}\)…
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