Chapter: - Matrix and Determinants: 1 Marks Question
Chapter: - Matrix and Determinants: 1 Marks Question
Chapter: - Matrix and Determinants: 1 Marks Question
com
4 2
Q2.IfA= then find (A-2I)(A-3I). Ans. 0 .
sin x cos x
1 1
Q3. Evaluate When x=π/6 Ans . -1/2.
cos x sin x
Q4.If for matrix A, A =3, Find 4 A , Where matrix A is of order 2x2. Ans. 48
1 0
1
Q5.Construct a 2x3 matrix whose element is given by aij = 3i j Ans.
3
1 2
5
2 2
2 2
cos x sin x
m
Q6.IfA= then find x such that A+A’=I. Ans. π/3.
sin x cos x
co
0 a 3
y.
Q7If A= 2 b 1 is a skew symmetric matrix, find the values of a,b and c. Ans . -2, 0,-3,
da
c 1 0
to
k
Q8.If A= [3 5], B= [7 3], then find non -zero matrix such that AC=BC. Ans. Where k is any real number.
es
2k ,
di
2 3 8
Q9. Solve for x,y such that x y 0 ,Ans. 1,2 Q10. If
2 x
tu
1 5 11
=0 then find x. Ans. ±2
x 2
.s
Q11. If 2 x 3
1 2 x
0 , find the value of x, Ans.-23/2.
w
3 0 8
w
w
Q12. The area of a triangle with vertices(-3,0),(3,0)and (0,k)is 9sq. units then find k Ans. 3.
Q13. Show that the points (a+5, a-4), (a-2, a+3) and (a, a) do not lie on straight line.
1 1 1
Q14.Find maximum value of 1 1 sin x 1 , Ans. 1/2
1 1 1 cos x
P.T.O.
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(vii)(A’)’=A (viii)((A’)’)’=A’(ix) AB≠BA (x)CD≠DC (xi)(AC)’=C’A’ (xii) (BD)’=D’B’ (xiii)(A-1)’=(A’)-1
xy 4 8 w
Q17.If = then find the values of x,y,z,w, Ans. 4,2 ,-6,-4 or2,4,-6,-4,
z 6 x y 0 6
1 3 5
6 7
Q18. Express (i) 6 8 3 (ii)
2 1
as a sum of symmetric and skew symmetric matrices.
4 6 5
3 1 9
1 2 2 5 9
9
3 9 9 3
0
6
2 + 2
2 2
Ans. (i) + , (ii) . 5 9
0
2 2 2 2 1 0 .
8 0
1 9
5 0 2 2
2 2
9 3
2 2
2 3 3
4 3 2 3
m
Q19.By ET find Inverse of (i) 1 2 2 Ans. Does not exist. (ii)
Ans.
3 2 3 4
co
1 1 1
y.
Q20.Using the matrix method solves the following system of linear equations. x+ y+z = 6, y +3 z =11, x + z = 2y,Ans. 1,2,3
da
1 0
Q21.If A= 2 1 2 find A-1 hence solve the system of following linear equations:-
2
to
0 1 1
es
di
2 2 4 1 1 0
Q22.If A= 4 2 4 and B=
2 3 4 find AB and BA hence solve the system of linear equations:-
.s
1 1 5 0 1 2
w
w
1 1 p 1 p q (a x ) 2 (a y ) 2 (a z ) 2
(i) 2 3 2 p 4 3 p 2q 1 (ii) (b x) (b y) 2 (b z ) 2 2(a-b) (b-c) (c-a) (x-y) (y-z) (z-x)
2
3 6 3 p 10 6 p 3q (c x ) 2 (c y ) 2 (c z ) 2
3a ab ac
(iii) b a 3b b c 3( a b c )( ab bc ca ) .
ca cb 3c
bc a 2 ca b 2 ab c 2
(iv) ca b ab c 2 bc a 2 (a b c)(a 2 b 2 c 2 ab bc ca) .
2
ab c 2 bc a 2 ca b 2
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