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DNA ACADEMY Time : 1hr Sub: Mathematics I Marks: 30 Std. 12 th Test : Matrices Q.1.(A) Write the correct answer from the given alternatives in each of the following (8) 1. A = 1 2 3 4 and A (adj A) = KI, then the value of ‘K’ is _______ (A) 2 (B) -2 (C) 10 (D) – 10 2. What is the size of the matrix A? A = [ 1 56 7 9 27 9 3 45 10 ] (A) 2 x 3 (B) 3 x 2 (C) 3 x 4 (D) 4 x 3 3. If A = [ 1 2 3 4 ] ∧ Xisa 2 X 2 ¿ hthatAX =I,thenXis (A) X= [ −1 −2 3 4 ] (B) X= [ −2 1 3 2 −1 2 ] (C) X= [ −5 0 2 4 ] (D) X= [ 3 4 1 2 ] 4. If the [ a ij ]mxm is non singular square matrix then its inverse exists and it is given as (A) A -1 = 1 |A| ( adjA ) (B) A −1 =( adj A )|A| (C) A −1 =2 ( adj A )|A| (D) A −1 = 1 | A| ( adj A ) 2 (B) Attempt any four of the following (8) 1. Find metrics A = [ cosθ sinθ −sinθ cosθ ] is invertible or not? 2. Find the metrics X such that AX = B , where A = [ 1 2 −1 3 ] ∧B= [ 0 1 2 4 ] 3. Find the adjoint of matrix A = [ 2 −3 4 1 ] 4. Find the inverse of the matrix B= [ 2 −3 −1 2 ] by using transformation method. 5. Find the matrix of cofactor for the matrix [ 1 3 4 −1 ]

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matrices 12th paper 30 marks

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DNA ACADEMYTime : 1hr Sub: Mathematics I

Marks: 30Std. 12th Test : Matrices

Q.1.(A) Write the correct answer from the given alternatives in each of the following (8)1. A = 1 2

3 4 and A (adj A) = KI, then the value of ‘K’ is _______(A) 2 (B) -2(C) 10 (D) – 10

2. What is the size of the matrix A?A=[1 56 79 27 93 45 10] (A) 2 x 3 (B) 3 x 2 (C) 3 x 4 (D) 4 x

3. If A=[1 23 4 ]∧X is a2 X 2¿h t hat AX=I , t hen X is

(A) X=[−1 −23 4 ] (B) X=[−2 1

−12 ] (C) X=[−5 0

2 4 ] (D)X=[3 41 2 ]

4. If the [a ij ]mxm is non singular square matrix then its inverse exists and it is given as

(A) A-1 = 1|A|(adj A) (B) A−1=(adj A )|A| (C) A−1=2 (adj A )|A| (D) A−1= 1|A|

(adj A )2

(B) Attempt any four of the following(8)

1. Find metrics A=[ cosθ sinθ−sinθ cosθ ] is invertible or not?

2. Find the metrics X such that AX = B , where A=[ 1 2−1 3 ]∧B=[0 1

2 4 ] 3. Find the adjoint of matrix A=[ 2 −3

4 1 ] 4. Find the inverse of the matrix B=[ 2 −3

−1 2 ] by using transformation method.

5. Find the matrix of cofactor for the matrix [1 34 −1]

Q.2. (A) Attempt any Three of the following(6)

1. Solve the equation 2x + 5y = 1 and 3x + 2y = 7 by the method of inversion.2. Solve the following equation by method of reduction x + y + z =1 ; 2x + 3y + 2z = 2 and x + y + 2z = 4.

3. Find the inverse of [1 2 31 1 52 4 7 ]by using elementary row transformation.

4. Find the A-1 by adjoint method [ 1 3 −2−3 0 −52 5 0 ]

(B) Attempt any TWO of the following (8)

1. The sum of three numbers is 9. If we multiply third number by 3 and add to the second number, we get 16. By adding the first and the third number and then subtracting twice the second number from this sum, we get 6. Use this information and find the system of linear equations. Hence, find the three numbers using matrices. (March 2013)2. The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is Rs. 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers Rs. 90, whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is Rs 70. Find the cost of each item per dozen by using matrices (March 2016) 3. If three numbers are added the sum is 15. If the second number is subtracted from the sum of first and third number then we get 5 and if twice the first number is added to the second and the third number is subtracted from the sum we get 4. Use matrices to find the numbers.