Home
Class 12
MATHS
If A=[1 3 2 1] , find the determinant of...

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

Text Solution

Verified by Experts

`A^2=A.A=[[1,3],[2,1]][[1,3],[2,1]]`
`[[1+6,3+3],[2+2,6+1]]=[[7,6],[4,7]]`
`A^2-2A=[[7,6],[4,7]]-2[[1,3],[2,1]]`
`=[[7-2,6-6],[4-4,7-2]]`
`=[[5,0],[0,5]]`
`|A^2-2A|=[[5,0],[0,5]]`
`=25-0`
`=25`
...
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=[1321], find the determinant of the matrix A^(2)-2A

If A=[[1,32,1]], find the determinant of the matrix A^(2)-2A

Find the determinant of a matrix [{:(2,-3),(4," "5):}]

Find the adjoint of the matrix: [(2,-1),(4,3)]

Find the adjoint of the matrix: [(1,2),(3,4)]

Find the adjoint of the matrix A=[[2,3],[1,4]] .

Find the adjoint of the matrix [[2,-2,42,3,2-1,1,-1]]

Find the adjoint of matrix A=[[2,-3],[4,1]]

if A=[[1,3,-40,2,1]] then find out transpose of matrix A.

find the transpose of the matrix A=[{:(1,3,-4),(0,2,1):}].

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

    Text Solution

    |

  2. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by two methods

    Text Solution

    |

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

    Text Solution

    |

  4. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 1x-...

    Text Solution

    |

  5. The value of the determinant |xx+y x+2y x+2y xx+y x+y x+2y x|i s 9x^2...

    Text Solution

    |

  6. Let f(x)=|[cosx , x , x] , [2sinx , x , 2x] , [sinx , x , x]|, then ...

    Text Solution

    |

  7. A triangle has its three sides equal to a , b and c . If the coordin...

    Text Solution

    |

  8. Solve the following system of equations using Cramers rule. 5x-7y+z=1...

    Text Solution

    |

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

    Text Solution

    |

  10. Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(...

    Text Solution

    |

  11. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

    Text Solution

    |

  12. |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A)...

    Text Solution

    |

  13. Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+...

    Text Solution

    |

  14. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

    Text Solution

    |

  15. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

    Text Solution

    |

  16. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

    Text Solution

    |

  17. If A(x1, y1),B(x2, y2) and C(x3,y3) are vertices of an equilateral ...

    Text Solution

    |

  18. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

    Text Solution

    |

  19. Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[...

    Text Solution

    |

  20. Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x,...

    Text Solution

    |