Home
Class 12
MATHS
A matrix A of order 3xx3 has determinant...

A matrix `A` of order `3xx3` has determinant 5. What is the value of `|3A|?`

Text Solution

Verified by Experts

`[A] _(3 xx 3) , |A| = 5`
`|3A| = ?`
`|nA| = n^P|A|`
(i) `|3A| = (3)^3 |A| = 27 xx5`
`= 135`
Answer
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

A matrix of order 3xx3 has determinant 2. What is the value of |A(3I)| , where I is the identity matrix of order 3xx3 .

If A is a square matrix of order 3 with determinant 4, then write the value of |-A| .

A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose ?

A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose ?

A matrix A of order 3xx3 is such that |A|=4 . Find the value of |2A| .

If A is any square matrix of order 3xx3 such that |A|=3 , then the value of |adjA| is ?

If A is any square matrix of order 3xx3 such that |A|=3 , then the value of |adjA| is ?

Given a square matrix A of order 3xx3 such that |A|=12 , find the value of |"A adj A"|

If A is a diagonal matrix of order 3xx3 is commutative with every square matrix or order 3xx3 under multiplication and tr(A)=12, then the value of |A|^(1/2) is

If A is a square matrix of order 3 such that |A|=5 , write the value of |a d j\ A| .

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Find the value of lambda for which the homogeneous system of equations...

    Text Solution

    |

  2. If the system of equations x=c y+b z y=a z+c x z=b x+a y has...

    Text Solution

    |

  3. A matrix A of order 3xx3 has determinant 5. What is the value of |3A|?

    Text Solution

    |

  4. If A is a square matrix such that |A|=2 , write the value of |AA^T|

    Text Solution

    |

  5. Find the real values of lambda for which the following system of linea...

    Text Solution

    |

  6. If a , b , c are non-zero real numbers and if the system of equations...

    Text Solution

    |

  7. Which of the following is not correct in a given determinant of A , wh...

    Text Solution

    |

  8. Let |(x,2,x),(x^2,x,6),(x,x,6)|=a x^4+b x^3+c x^2+dx+edot Then, the va...

    Text Solution

    |

  9. Let △=|(A x,x^2, 1),(B y, y^2, 1),(C z, z^2, 1)| and△1=|(A,B, C),( x, ...

    Text Solution

    |

  10. If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

    Text Solution

    |

  11. Without expanding show that: =|cos e c^2thetacot^2theta1cot^2thetacos ...

    Text Solution

    |

  12. Find the value of the determinant =|2 3 4 5 6 8 6x9x 12 x|dot

    Text Solution

    |

  13. Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

    Text Solution

    |

  14. Show that matrix |(1,a,b+c),(1,b,c+a),(1,c, a+b)|=0

    Text Solution

    |

  15. Without expanding evaluate the determinant |(x^2+x^(-1))^2(a^2-a^(-1))...

    Text Solution

    |

  16. If 1=|(1, 1, 1),(x^2,y^2,z^2),(x, y ,z)|a n d2=|(1 ,1, 1),(y z, z x,x ...

    Text Solution

    |

  17. Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

    Text Solution

    |

  18. Without expanding evaluate the determinant |[sinalpha,cosalpha,sin(alp...

    Text Solution

    |

  19. If A+B+C=pi, then the value of |[sin(A+B+C),sin(A+C),cosC],[-sinB,0...

    Text Solution

    |

  20. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

    Text Solution

    |