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प्रश्न
If A and B are invertible matrices, which of the following statement is not correct.
पर्याय
\[adj A = \left| A \right| A^{- 1}\]
\[\det \left( A^{- 1} \right) = \left( \det A \right)^{- 1}\]
\[\left( A + B \right)^{- 1} = A^{- 1} + B^{- 1}\]
\[\left( AB \right)^{- 1} = B^{- 1} A^{- 1}\]
उत्तर
\[\left( A + B \right)^{- 1} = A^{- 1} + B^{- 1}\]
We have, \[adj A = \left| A \right| A^{- 1}\], \[\det \left( A^{- 1} \right) = \left( \det A \right)^{- 1}\] and \[\left( AB \right)^{- 1} = B^{- 1} A^{- 1}\] all are the properites of inverse of a matrix.
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संबंधित प्रश्न
Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. School A wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively with a total award money of Rs 1,600. School B wants to spend Rs 2,300 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for an award.
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| To raise money for an orphanage, students of three schools A, B and C organised an exhibition in their residential colony, where they sold paper bags, scrap books and pastel sheets made by using recycled paper. Student of school A sold 30 paper bags, 20 scrap books and 10 pastel sheets and raised ₹ 410. Student of school B sold 20 paper bags, 10 scrap books and 20 pastel sheets and raised ₹ 290. Student of school C sold 20 paper bags, 20 scrap books and 20 pastel sheets and raised ₹ 440. |
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- Hence, find the cost of one paper bag, one scrap book and one pastel sheet.
