Home
Class 12
MATHS
A matrix A of order 3x3 has determinant ...

A matrix `A` of order `3x3` has determinant 5. What is the value of `|3A|?`

Text Solution

AI Generated Solution

To find the value of \(|3A|\) where \(A\) is a \(3 \times 3\) matrix with \(|A| = 5\), we can use the property of determinants related to scalar multiplication. ### Step-by-step Solution: 1. **Understand the property of determinants**: For a square matrix \(A\) of order \(n\) and a scalar \(k\), the determinant of the scaled matrix \(kA\) is given by: \[ |kA| = k^n |A| \] ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos
  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 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| .

Let A be the the square matrix of order 3 and deteminant of A is 5 then find the value of determinant of adj(A)

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

If A is a square matrix of order 3 such that |A| =3 then find the value of |(a d j A)|

If A is a square matrix of order 3 such that |A|=3 , then write the value of | adj A|

If A is a square matrix of order 3 such that |A|=2 , then write the value of |(a d jA)|

If A is square matrix of order, 3, with |A| = 4, then write the value of |-2A|.

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  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 3x3 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 |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3...

    Text Solution

    |

  9. Let delta=|A x x^2 1 B y y^2 1 C z z^2 1|a n d1=|A B C x y z y z z xx ...

    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: =|(cose c^2theta,cot^2theta,1),(cot^2thet...

    Text Solution

    |

  12. Find the value of the determinant =|(2, 3, 4),( 5, 6, 8),( 6x,9x ,12 x...

    Text Solution

    |

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

    Text Solution

    |

  14. Show that |1a bc1b c+a1c a+b|=0

    Text Solution

    |

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

    Text Solution

    |

  16. If D1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D2=|[1, 1, 1],[yz, zx,xy...

    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

    |