Mathematics Test 75

Result

Mathematics Test 75

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Weekly Quiz Competition

Question 1
4 / -1

If A is skew symmetric matrix such that A² – I = 0 then order of A is :

A
even order

B
odd order

C
any order

D
None of these

Solution

A² = + I ⇒ |A| = ± 1 ⇒ order is even.
Question 2
4 / -1

If A is diagonal matrix of order 3 × 3 is commutative with every square matrix of order 3 × 3 under multiplication and trace (A) = 12, then |A| is equal to

A
64

B
16

C
12

D
0

Solution

A diagonal matrix is commutative with every square matrix if it is scalar matrix so every diagonal element is 4, so |A| = 64.
Question 3
4 / -1

A square matrix P satisfies P² = I – P, If Pⁿ = 5I – 8P then n is :

A
4

B
5

C
6

D
7

Solution

P⁴ = (I – P) (I – P) = I – 2P + P² = 2I – 3P

P⁶ = (2I – 3P) (I – P) = 5I – 8P Þ n = 6
Question 4
4 / -1

A and B are two square matrix such that A²B = BA and if (AB)¹⁰ = A^kB¹⁰ then k is

A
10

B
1001

C
1023

D
1042

Solution

(AB)² = (AB) (AB) = A(BA) B = A³B²

Now (AB)³ = AB AB AB = A⁷B³

So (AB)ⁿ = (A)^2n-1Bⁿ

so k = 2¹⁰ – 1 = 1023