DPPS
PRACTICE PROBLEM SHEET Mathematics
Matrix
Triangular Matrix:Q.1Find an upper triangular matrix A such that
A3 =
(1)
(2)
(3)
(4) None of these
Trace of matrix:
Q.2Let A + 2B = and 2A B=. Then tr(A) tr(B) has the value equal
to-
(1) 0(2) 1 (3) 2
(4) None of these
Matrix multiplication and its properties:
Q.3If A, B are square matrices such that A2 = A, B2 = B, and A,
B commute then-
(1) (AB)2 = I(2) (AB)2 = AB (3) (AB)2 = O(4) None of these
Positive integer power of matrix:
Q.4If A =. Let An = [bij]22. Define An = [bij]22. Then
EMBED Equation.3 =
(1) zero matrix(2) unit matrix (3)
(4) Limit doesn't exist
Q.5If A = and B = . Then A8 equals-
(1) 128B(2) 128B(3) 4B(4) 64B
Q.6Define A = . Find a vertical vector V such that (A8 + A6 + A4
+ A2 + I) V =
(where I is the 2 2 identity matrix)
(1)
(2) (3)
(4) None of these
Transpose of matrix:
Q.7If 3A = and AA= I then x + y is equal to-
(1) 5(2) 4(3) 3(4) 2
Adjoint of a Matrix:
Q.8If A = , then adj A is equal to
(1) A(2) AT(3) 3A(4) 3AT
Inverse of Matrix and its properties:Q.9If =. then the value of
x is
(1)
(2)
(3)
(4) None
Q.10If the matrices A, B, A + B are non singular, then [A(A +
B)1B]1, is equal to
(1) A1 + B1(2) A + B(3) A(A + B)1(4) None of these
Q.11If A() = and AB = I, then (sec2) B is equal to
(1) A() (2) A() (3) A(/2) (4) A(/2)
Q.12If AB = BA and C2 = B, then [A1CA]2 is equal to-
(1) C(2) B(3) A(4) None
Answers :1.[3]
Let A =; A2 = ;
A3 = =
a = 2,c = 3, b = 32.[3]
tr(A) + 2tr(B) = 1
2tr(A) tr(B) = 3
tr(A) = 1, tr(B) = 1
tr(A) tr(B) = 2
3.[2]
(AB)2 = (AB) (AB) = A(BA) B
= A(AB)B
( AB = BA)
= A2 B2 = AB
4.[1] An =
EMBED Equation.3 =
5.[1]
A2 = B2
A2 = = 2B
A4 = (2B)2 = 4B2 = 4(2B) = 8B
A8 = 64B2 = 128B6.[1]
A2 = 3I ; A4 = A2.A2 = 9I ; A6 = 27I; A8 = 81I
(81+27+9+3+1) IV =
121 V = ; V =
7.[3]
3A 3A =
= 9
x + 2y + 4 = 0
2x 2y + 2 = 0
We get x = 2, y = 1
x + y = 3
8.[4]
adj (A) = = 3
9.[1]
Let A =; A1 =
EMBED Equation.3
A2 =
x =
10.[1]
[A(A + B)1 B]1
= B1(A + B) A1
= (B1A + I) A1 = B1 + A111.[2]
B = A1 =
EMBED Equation.3
(sec2) B =
(sec2 B = A()
12.[2]
[A1 CA]2 = [A1 CA] [A1 CA]
= A1 C(AA1) CA
= A1C2A
= A1BA
= B
DPPS No. - 01
PRE ENGINEERING
CP Live Enthuse Class XII -2015
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