Home
Class 12
MATHS
Let M and N be two 3xx3 matrices such th...

Let M and N be two `3xx3` matrices such that `MN=NM`. Further, if `M ne N^(2)` and `M^(2)=N^(4)`, then

A

`|M^2N^2+M^2+MN^4|=0`

B

There exist a non zero 3 × 1 matrix U such that `(M^2N^2+M^3 +MN^4)`U is a zero matrix

C

`|M^2N^2+M^3+MN^4| ge 1`

D

For a 3 x 1 matrix U such that `(M^2N^2 + M^3+MN^4)U` is a zero matrix then U is a zero matrix

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|92 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and M^2=N^4 then which of the following are correct.

Let Ma n dN be two 3xx3 non singular skew-symmetric matrices such that M N=N Mdot If P^T denote the transpose of P , then M^2N^2(M^T N^(-1))^T is equal to M^2 b. -N^2 c. -M^2 d. M N

Let M and N are two non singular matrices of order 3 with real entries such that (adjM)=2N and (adjN)=M . If MN=lambdaI , then the value the values of lambda is equal to (where, (adj X) represents the adjoint matrix of matrix X and I represents an identity matrix)

If A and B are two matrices of the order 3 xx m and 3 xx n , respectively and m= n, then order of matrix (5A-2B) is (a) m xx 3 (b) 3 xx 3 (c) m xx n (d) 3 xx n

If A and B are two matrices of the order 3 xx m and 3 xx n , respectively and m= n, then order of matrix (5A-2B) is (a) m xx 3 (b) 3 xx 3 (c) m xx n (d) 3 xx n

Let M be a 3xx3 matrix satisfying M^(3)=0 . Then which of the following statement(s) are true: (a) |M^(2)+M+I|ne0 (b) |M^(2)-M+I|=0 (c) |M^(2)+M+I|=0 (d) |M^(2)-M+I|ne0

Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n)

If A and B are two matrices of order 3 xx m and 3 xx n respectively, and m = n, then the order of matrix (5A - 2B) is

Prove that (mn)! Is divisible by (n!)^(m) " and" (m!)^(n) .

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -LEVEL 2
  1. A is even ordered non singular symmetric matrix and B is even ordered ...

    Text Solution

    |

  2. If P is a 3xx3 matrix such that P^(T) = 2 P + I , where P^(T) is the...

    Text Solution

    |

  3. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c...

    Text Solution

    |

  6. A=[[0 ,1],[ 3 ,0]]a n d(A^8+A^6+A^4+A^2+I) V=[[0] ,[11]](w h e r eIi s...

    Text Solution

    |

  7. If [(a,b),(c,1-a)] is an idempotent matrix and f(x)=x-x^(2) and bc=1//...

    Text Solution

    |

  8. Let x be the solution set of equation A^x=Idot,w h e r eA+[0 1-1 4-3 4...

    Text Solution

    |

  9. A=[(1,tan x),(-tan x,1)] and f(x) is defined as f(x)= det. (A^(T)A^(-1...

    Text Solution

    |

  10. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

    Text Solution

    |

  11. Let A=[(3x^(2)),(1),(6x)], B=[(a,b,c)], and C=[((x+2)^(2),5x^(2),2x)...

    Text Solution

    |

  12. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

    Text Solution

    |

  13. Let S be the set which contains all possible values of l, m, n, p, q, ...

    Text Solution

    |

  14. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

    Text Solution

    |

  15. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. The sum of roots of the equations |{:(x+2,,2x+3,,3x+4),(2x+3,,3...

    Text Solution

    |

  18. If alpha,beta,gamma are real numbers, then without expanding at any...

    Text Solution

    |

  19. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

    Text Solution

    |

  20. Express =|2b c-a^2c^2b^2c^2 2c a-b^2a^2b 62a^2 2a b-c^2| as square of ...

    Text Solution

    |