Matrices Test

Result

Matrices Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

. The only correct statement about the matrix A is

A
A^–1 does not exist

B
A = (-1) I, where I is a unit matrix

C
A is a zero matrix

D
A² = 1
Question 2
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Let the determinant of a 3 x 3 matrix A be 6. If B is a matrix defined by B = 5A², then the determinant of B is

A
180

B
100

C
80

D
None of these
Question 3
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If A = and A² =

A

B

C

D
Question 4
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where f(x) is characteristic polynomial of A

Find the wrong statement about A.

A
A³ is invertible.

B
A² is invertible.

C
A² - 4A is invertible

D
A³ - 3A² - 9A - 5I is invertible.

Question 5

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Directions: Match the statements/expressions in Column - I with the statements/expressions in Column - II and indicate your answer by selecting the appropriate option. Any statement in Column - I can correctly match with one or more statement(s) in Column - II.

A	If A =	P	3
B	There are 7 green bottles and 8 blue bottles (assume all bottles to be alike except for the colour) arranged in a row. If exactly one pair of green bottles is side by side in 7^m. 3ⁿ. 2^r ways, the value of m + n + r =	Q	2
C	If w is primitive cube root of unity, then the period of is	R	6
D	If a, b and c are sides of a triangle satisfying a² + b² + c² – ac – ab = 0, then	S	5

A Q; B R; C P; D P

A Q; B R; C S; D P

A Q; B R; C P; D S

A R; B Q; C P; D S

Question 6

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Directions: Match the statements / expressions in Column-I with the statements / expressions in Column-II and indicate your answer by selecting the appropriate option. Any statement in Column -I can correctly match with one or more statement(s) in Column -II.

Column - I

Column - II

A	Determinants of order 2 × 2 are formed using the numbers 0, 1, 2, 3. Then, sum of values of all such determinants is	P	-1
B	If is orthogonal, the value of	Q	2
C	If ^,where [.] denotes g.i.f,	R	-2
D	Product of all value of is	S	0
		T	1

A S; B T; C P, R, S; D P

A R; B T; C P, R, S; D S

A S; B T; C P, R, S; D R

A Q; B T; C P, R, S; D P

Question 7

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Column - I

Column - II

A	If and find the value of 5a + b	P	5
B	If and B is inverse of A, then a =	Q	1
C	If ^, then the value of c + d is	R	4
D	If A = , , then =	S	3

A Q; B P; C P; D S

A P; B Q; C P; D S

A R; B P; C Q; D S

A S; B P; C R; D Q

Question 8
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If A =and f(x) = 1 + x + x² + .... + x¹⁶, then f(A) is equal to

A
0

B

C

D
Question 9
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If A and B are 3 3 matrices such that AB = B and BA = A, then

A
A² = A and B² B

B
A² A and B² = B

C
A² = A and B² = B

D
A² A and B² B
Question 10
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If A = and B = A + A² + A³ + A⁴, which of the following statements is/are correct?

A
B is symmetric

B
B is invertible

C
A is periodic

D
All of the above

E
None of these
Question 11
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Directions: The following question has four choices, out of which ONE or MORE is/are correct.

Let A be a 3 3 Hermitian matrix with complex elements, while P and Q be two 3 3 matrices with real elements. If A = P + iQ, then

A
P must be symmetric

B
Q must be symmetric

C
P must be skew-symmetric

D
Q must be skew symmetric
Question 12
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Directions: Choose the correct option(s).

If , and , then wrong statement(s) is/are

A
A(z) = A(x) + A(y)

B
A(z) = A(x) – A(y)

C
A(z) = A(x) (A(y))^–1

D
Question 13
1 / -0

Directions: The following question has four choices, out of which ONE or MORE is/are correct.

If A = and A³ + aA² + bA + cI = 0, f(x) = ax² + bx + c, then the equation f(x) = 0 has

A
a pair of irrational roots

B
a pair of complex roots

C
unequal roots

D
real roots