Home
Class 12
MATHS
If matrix A=[1,2,3] , find AA^T ....

If matrix `A=[1,2,3]` , find `A``A^T` .

Text Solution

Verified by Experts

Given that,
`A=[[1,2,3]]`
`A^T=[[1],[2],[3]]`
`=A A^T=[[1,2,3]] [[1],[2],[3]]`
`1 times underbrace(3. 3) times 1=1 times 1`
`[1 times 1+ 2 times 2 +3 times 3]`

`[1+4+9]`

...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

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

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

For the matrix A = [(2,-3),(-5,7)] , (A+ A^T) is a:

For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0 . Hence find A^(-1)

If A=[[2,5],[1,3]],B=[[4,-2],[-1,3]] and I is the identity matrix of the same order and A^T is transpose of matrix A then find A^(T)B+BI

Find the inverse of the matrix [{:(-3,2),(5,-3):}] Hence, find the matrix P satisfying the matrix equation : P[{:(-3,2),(5,-3):}]=[{:(1,2),(2,-1):}]

(2) Find the rank of the matrix A=[[1,2,3,-1],[3,6,9,-3],[2,4,6,-2]]

(a) Find the inverse of the matrix A=[[1,1,1],[1,2,-3],[2,-1,3]]

" If matrix "A=[[1,1,3],[1,3,-3],[-2,-4,-4]]" then find "A^(-1)

Find the inverse of the matrix A=[[1,2,3],[2,4,5],[3,5,6]] by using elementary raw transformations

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Find the value of y, if [(x-y,2),(x,5)]=[(2, 2 ),(3, 5)].

    Text Solution

    |

  2. Find the value of x , if [(3x+y,-y),(2y-x,3)]=[(1, 2),(-5, 3)] .

    Text Solution

    |

  3. If matrix A=[1,2,3] , find AA^T .

    Text Solution

    |

  4. If [(2x+y,3y),(0, 4)]=[(6, 0),( 6, 4)] , then find x .

    Text Solution

    |

  5. If A=[(1, 2 ),(3, 4)] , find A+A^T .

    Text Solution

    |

  6. If [(a+b,2),( 5,b)]=[(6, 5),( 2, 2)] , then find adot

    Text Solution

    |

  7. If A is a matrix of order 3xx4 and B is a matrix of order 4xx3 , find ...

    Text Solution

    |

  8. If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] is identity matrix, t...

    Text Solution

    |

  9. If [(1, 2),( 3, 4)][(3, 1),( 2, 5)]=[(7, 11),( 23, k)] , then write t...

    Text Solution

    |

  10. If I is the identity matrix and A is a square matrix such that A...

    Text Solution

    |

  11. If A=[(1, 2),( 0, 3)] is written as B+C , where B is a symmetric matri...

    Text Solution

    |

  12. If A is 2 times 3 matrix and B is a matrix such that A^T\ B and B A^T ...

    Text Solution

    |

  13. What is the total number of 2xx2 matrices with each entry 0 or 1...

    Text Solution

    |

  14. If [[x,x-y],[2x+y,7]]=[[3 ,1],[ 8, 7]] , then find the value of y

    Text Solution

    |

  15. If a matrix has 5 elements, write all possible orders it can have.

    Text Solution

    |

  16. For a 2xx2 matrix A=[a(i j)] whose elements are given by a(i j)=i/j...

    Text Solution

    |

  17. If x [[2 ],[3]]+y[[-1],[ 1]]=[[10],[ 5]] , find the value of x

    Text Solution

    |

  18. If [[9,-1, 4],[-2, 1, 3]]=A+[[1 ,2,-1],[ 0, 4, 9]] , then find matrix ...

    Text Solution

    |

  19. If [(a-b,2a+c),(2a-b,3c+d)]=[(-1, 5),( 0, 13)] , find the value of b

    Text Solution

    |

  20. For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-...

    Text Solution

    |