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Phoenix Institute of Mathematics Jalgaon, , Dhamaka-5, , DATE:, TIME: 1 Hours, MARKS: 25, , 12th Science- 2020 : Maths, Matrics,, SEAT NO:, , Note:-, , 1. All Questions are compulsory., 2. Numbers on the right indicate full marks., , Section A, , Q.1 Select and write the correct answer., 1., , (4), , find AAT ., , If, A) Zero matrix, , B) I2, , C), , D) None of these, , 2., then, , If, , A), , B), , C), , D), , is equal to, , Q.2 Answer the following., , (3), , 1., Check whether the matrix, , is invetible or not., , 2., Check whether the matrix, 3., , Check whether the matrix, , is invertible or not., , is invertible or not., , Section B, Attempt any Four, , Q.3, , Solve the given equations by the reduction method., x + 3y = 2, 3x + 5y = 4, , (2)

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Q.4, Q.5, , Convert, , into an identity matrix by suitable row transformations., , (2), , Solve the given equations by the reduction method., 3x – y = 1, 4x + y = 6, , Q.6, , (2), ,, , Q.7, , (2), , and then, , Find the inverse of the, , matrix (if they exist)., , Q.8, , (2), (2), , If, , –1, , is a nonsingular matrix then find A by elementary row transformations., , Hence, find the inverse of, , ., Section C, Attempt any Two, , Q.9, , Find the inverse of the, , matrix (if they exist)., , Q.10, , (3), Find the inverse of the matrix, , Q.11, , (3), , (if they exist) ., , The sum of three numbers is 2. If twice the second number is added to the sum of first and, third number, we get o adding five times the first number to the sum of second and third we, get 6. Find the three numbers by using matrices., , (3), , Section D, Attempt any One, , Q.12, , (4), Find the inverse of the, , Q.13, , matrix (if they exist)., , The cost of 4 pencils, 3 pens and 2 books is Rs.150. The cost of 1 pencil, 2 pens and 3 books is, Rs.125. The cos of 6 pencils, 2 pens and 3 books is Rs.175. Find the cost of each item by using, matrices., , (4)