ZAKARIYA EDUCATIONAL SYSTEM LAYYAH

ZAKARIYA EDUCATIONAL SYSTEM LAYYAH

Paper: Math Class: 1^st Year   T # 5  (G.T.S-2022)   T.M: 50   Date:03-03-22  Time: 1.30h

(Subjective)

Q. No. 2: Short Questions                                                                    (2×10=20)

1.       Show that = 9

2.       Show that=  r

3.       If A = then find (A^t)^-1

4.       If  A =  then findA

5.       Find values of x if = 0

6.       If A is a square matrix of order 3, then show that |kA| = k³ |A|

7.      find the values of l if A is singular A  = 

8.      Find whether the given matrix is singular or non-singular

9.       Without expansion verify that = 0

10.   Without expansion verify that= 0

Long Questions                                                    (5×4=20)

1.       Show that = (x + 3)(x – 1)

2.       If B = , then findB , B , B and        

3.       Solve system of linear equations by Cramer’s rule

2x  + 2y + z=  3 ; 3x  – 2y  – 2z =  1 ; 5x + y  – 3z       =  2

4.       Solve system of homogeneous linear equations

x + 2y - 2z = 0 ;2x +   y + 5z = 0 ; 5x + 4y + 8z = 0

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ZAKARIYA EDUCATIONAL SYSTEM LAYYAH

Paper: Math Class: 1^st Year   T # 5  (G.T.S-2022)   T.M: 50   Date:03-03-22  Time: 1.30h

 

(Objective)

Q.No.1   Choose the correct option.                                                    (10)

1.If two rows (or two columns) in  a square matrix are identical (i.e. corresponding elements are equal), the value of the determinant is

(a) 0                                   (b)1                             (c) – 1                          (d) ± 1

2.If two rows (or two columns) in  a square matrix are identical (i.e. corresponding elements are equal), the value of the determinant is

(a) 0                                   (b) 1                            (c) – 1                          (d) ± 1

3.If any two rows of a square matrix are interchanged, the determinant of the resulting matrix is

(a)   zero                 (b) same                      (c) negative                 (d) positive

4.If A and B are non-singular matrices, then   =      

(a)   BA                    (b)  AB              (c)                 (d) Zero

5.Let  be a square matrix. Then the cofactor of adenoted  by A is defined as

(a)   M  (b) M      (c) M                     (d) M

6.Minors and co-factors of the elements in a determinant are equal in magnitude but differ in

(a)         order                     (b) position                    (c)sign                         (d) symmetry

7.If A is a square matrix, then

(a)         = A              (b) = –A               (c) =              (d) A = A

8.If each element of 3 ´ 3 matrix A is multiplied by 3, then the determinant of the resulting matrix is

(a)                                (b)27                                    (c)3                                    (d) 9

9.The value of is

(a)         ah + bg + cm        (b)ab + c d +  fgh                       (c)abcd                        (d) a + b + c + d

10.  In the homogeneous system of linear equations AX=O if ≠0 then the system has

(a)         no solution                                                   (b)infinitely many solutions

(b)         only trivial solution (0, 0, 0)                       (d) one trivial and one non-trivial solution