Home
Class 12
MATHS
Which of the following is(are) NOT of th...

Which of the following is(are) NOT of the square of a `3xx3` matrix with real enteries?

A

`[(1,0,0),(0,1,0),(0,0,-1)]`

B

`[(1,0,0),(0,-1,0),(0,0,-1)]`

C

`[(-1,0,0),(0,-1,0),(0,0,-1)]`

D

`[(1,0,0),(0,1,0),(0,0,1)]`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`A=B^(2)implies |A|=|B|^(2)=`+ve
(1) `|(1,0,0),(0,1,0),(0,0,-1)|=1(-1) lt 0`
Matrix B can not possible.
(2) `|(1,0,0),(0,-1,0),(0,0,-1)|=1 (1-0) gt 0`
(3) `|(-1,0,0),(0,-1,0),(0,0,-1)|=-1 lt 0`
Matrix B can not be possible.
(4) `|(1,0,0),(0,1,0),(0,0,1)|=1 gt 0`
Matrix B can be `I` (identity matrix).
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE ENGLISH|Exercise Linked Comprehension Type|27 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise Matrix Type|5 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise Exercises|65 Videos

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

Which of the following is (are) NOT the square of a 3xx3 matrix with real entries ?

Which of the following is correct (A) Determinant is a square matrix. (B) Determinant is a number associated to a matrix. (C) Determinant is a number associated to a square matrix. (D) None of these

Find the total number of possible square matrix. A order 3 with all real entries, with all real entries, whose adjoint matrix B has characteristics polymnomial equaltion, lambda^(3)-lambda^(2)+lambda+1=0.

D is a 3xx3 diagonal matrix. Which of the following statements are not true?

If one of the eigenvalues of a square matrix a order 3xx3 is zero, then prove that det A=0 .

Let psi_A be defined as trace of a matrix A which is sum of diagonal elements of a square matrix. Which of the following is true?

A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| Also |A^T|=|A| and for any two square matrix A d B of same order \AB|=|A||B| On the basis of above information answer the following question: IF A is a 3xx3 orthogonal matrix such that |A|=1, then |A-I|= (A) 1 (B) -1 (C) 0 (D) none of these

Let A be a square matrix. Then which of the following is not a symmetric matrix -

Let A,B and C be square matrices of order 3xx3 with real elements. If A is invertible and (A-B)C=BA^(-1), then

CENGAGE ENGLISH-MATRICES-Multiple Correct Answer
  1. Let B is an invertible square matrix and B is the adjoint of matrix A ...

    Text Solution

    |

  2. First row of a matrix A is [1,3,2]. If adj A=[(-2,4,alpha),(-1,2,1),...

    Text Solution

    |

  3. Let A be a square matrix of order 3 satisfies the relation A^(3)-6A^(2...

    Text Solution

    |

  4. Which of the following matrices have eigen values as 1 and -1 ? (a) [...

    Text Solution

    |

  5. Let Ma n dN be two 3xx3 non singular skew-symmetric matrices such that...

    Text Solution

    |

  6. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  7. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

    Text Solution

    |

  8. Let M be a 2xx2 symmetric matrix with integer entries. Then M is inver...

    Text Solution

    |

  9. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

    Text Solution

    |

  10. Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric ma...

    Text Solution

    |

  11. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  12. Which of the following is(are) NOT of the square of a 3xx3 matrix with...

    Text Solution

    |

  13. Let S be the set of all column matrices [(b(1)),(b(2)),(b(3))] such th...

    Text Solution

    |

  14. If A=[{:(1,0,0),(1,0,1),(0,1,0):}], then

    Text Solution

    |

  15. If the elements of a matrix A are real positive and distinct such that...

    Text Solution

    |

  16. If A=[{:(8,-6,2),(-6,7,-4),(2,-4,3):}] and X is a non zero column matr...

    Text Solution

    |

  17. If A, B are two square matrices of same order such that A+B=AB and I i...

    Text Solution

    |

  18. If A is a non-singular matrix of order nxxn such that 3ABA^(-1)+A=2A^(...

    Text Solution

    |

  19. If the matrix A and B are of 3xx3 and (I-AB) is invertible, then which...

    Text Solution

    |

  20. If A is a square matrix such that A*(AdjA)=[{:(4,0,0),(0,4,0),(0,0,4):...

    Text Solution

    |