Home
Class 12
MATHS
If A=[1 2 4 2] , then show that |2A|=4|A...

If `A=[1 2 4 2]` , then show that `|2A|=4|A|` .

Text Solution

Verified by Experts

`A=[( 1,2),(4,2)]`
`|A|=|(1,2),(4,2)|`
`=1xx2−4xx2=2−8=−6`
`4|A|=4×−6=−24 ldots(i)`
`|2A|=|(2,4),(8,2)|`
`=2 xx 2−4 xx 8`
`|2A|=8−32=−24 ldots (ii)`
from (i) and (ii)
...
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

If A=[[1,24,2]], then show that |2A|=4|A|

If A=|[1,2],[3,2]| ,then show that |2A|=4|A|

" 2.If "A=|[1,2],[4,2]|," then show that "|2A|=2|A|

If A=[[5,-4],[2,-1]] then show that |A| = |A^(T)|

If A=[{:(2,1,1),(1,2,1),(1,1,2):}] , then show that : |4A|=64|A| .

If A=[[2,4],[-5,-1]] show that: |3A|=9|A|

If sin A+sin^(2)A=1, then show that cos^(2)A+cos^(4)A=1

If A=[(3,-3,4),(2,-3,4),(0,-1,1)]2-3 41 then show that A^-1=A^1.

If A=[2-3-5-1 4 5 1-3-4] and B=[2-2-4-1 3 4 1-2-3] , show that A B=A and B A=B .

If A=[[ 1 ,4 , 7 ] , [2 , 5 , 8 ]] and B=[[-3, 4 , 0 ],[ 4 ,-2 , -1 ]] then show that ( A + B )^T = A^T + B^T

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

    Text Solution

    |

  2. If A=[1 3 2 1] , find the determinant of the matrix A^2-2A .

    Text Solution

    |

  3. If A=[1 2 4 2] , then show that |2A|=4|A| .

    Text Solution

    |

  4. If |x-2-3 3x2x|=3 , find the values of xdot

    Text Solution

    |

  5. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

    Text Solution

    |

  6. Evaluate the determinant =|(log)3 512(log)4 3(log)3 8(log)4 9| .

    Text Solution

    |

  7. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

    Text Solution

    |

  8. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

    Text Solution

    |

  9. If [ ] denotes the greatest integer less than or equal to the real nu...

    Text Solution

    |

  10. Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),...

    Text Solution

    |

  11. Write the minors and cofactors of each element of the first column ...

    Text Solution

    |

  12. Write the minors and cofactors of each element of the first column ...

    Text Solution

    |

  13. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  14. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  15. Evaluate: |2 3 7 13 17 5 15 20 12|^2 .

    Text Solution

    |

  16. Show that |sin10o-cos10osin80ocos80o|=1

    Text Solution

    |

  17. Evaluate |2 3-5 7 1-2-3 4 1| by two methods.

    Text Solution

    |

  18. Evaluate: =|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

    Text Solution

    |

  19. Evaluate: =|cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sin...

    Text Solution

    |

  20. If A=[2 5 2 1] and B=[4-3 2 5] , verify that |A B|=|A||B| .

    Text Solution

    |