Home
Class 12
MATHS
For alpha, beta, gamma in R, let A=[(a...

For `alpha, beta, gamma in R`, let
`A=[(alpha^(2),6,8),(3,beta^(2),9),(4,5,gamma^(2))]` and `B=[(2alpha,3,5),(2,2beta,6),(1,4,2gamma-3)]`

Text Solution

AI Generated Solution

To solve the problem, we need to find the values of \( \alpha \), \( \beta \), and \( \gamma \) such that the trace of matrix \( A \) is equal to the trace of matrix \( B \). Let's proceed step by step. ### Step 1: Write down the matrices \( A \) and \( B \) The matrices are given as follows: \[ A = \begin{pmatrix} ...
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE ENGLISH|Exercise CAE 13.1|5 Videos
  • MATRICES

    CENGAGE ENGLISH|Exercise CAE 13.2|6 Videos
  • MATRICES

    CENGAGE ENGLISH|Exercise Single correct Answer|34 Videos
  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos
  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

Three matrices are given as A = [{:( alpha ^(2) ,4,6),(9,beta ^(4) , 7),( 1,2,2gamma ^(2)):}] B= [{:( 2beta ^(2),-1,0),( 2,gamma^(2)-2gamma ,1),( 1,9,2alpha-1):}] C= [{:( gamma , 2,1),(1,alpha , 1),(2,0,beta ) :}] If Tr(A)=Tr (B) -1 and alpha, beta , gamma in R then det( c) can be

If roots of x ^(3) +2x ^(2) +1=0 are alpha, beta and gamma, then the vlaue of (alpha beta)^(3) + (beta gamma )^(3) + (alpha gamma )^(3) , is :

If alpha , beta , gamma are the roots of x^3 + px^2+qx -r=0 then alpha^2 + beta^2 + gamma^2 =

If alpha, beta and gamma the roots of the equation x^(3) + 3x^(2) - 4x - 2 = 0. then find the values of the following expressions: (i) alpha ^(2) + beta^(2) + gamma^(2) (ii) alpha ^(3) + beta^(3) + gamma^(3) (iii) (1)/(alpha)+(1)/(beta)+(1)/(gamma)

if alpha, beta, gamma are the roots of the equation x^(3) + 3x + 2=0 " then " (alpha^(3) +beta^(3)+gamma^(3))/(alpha^(2) +beta^(2)+gamma^(2))

If alpha , beta , gamma are the roots of x^3 +2x^2 +3x +8=0 then (3-alpha )(3 - beta) (3-gamma) =

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

If 2x^(3) + 3x^(2) + 5x +6=0 has roots alpha, beta, gamma then find alpha + beta + gamma, alphabeta + betagamma + gammaalpha and alpha beta gamma

If alpha, beta, gamma are the roiots of x^(3) - 10x^(2) +6x - 8 = 0 then alpha^(2) + beta^(2) + gamma^(2) =

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

CENGAGE ENGLISH-MATRICES-ILLUSTRATION
  1. If a square matix a of order three is defined A=[a("ij")] where a("ij"...

    Text Solution

    |

  2. For what values of x and y are the following matrices equal ? A=[(2x...

    Text Solution

    |

  3. For alpha, beta, gamma in R, let A=[(alpha^(2),6,8),(3,beta^(2),9),(...

    Text Solution

    |

  4. Find the values of x for which matrix [(3,-1+x,2),(3,-1,x+2),(x+3,-1,2...

    Text Solution

    |

  5. If A=[(1,2),(3,4),(5,6)] and B=[(-3,-2),(1,-5),(4,3)], then find D=[(p...

    Text Solution

    |

  6. A=[(cos alpha,-sin alpha),(sin alpha,cos alpha)] and A+A^(T)=I, find t...

    Text Solution

    |

  7. Let A be a square matrix. Then prove that (i) A + A^T is a symmetric m...

    Text Solution

    |

  8. If A=[(2,-1),(3,1)] and B=[(1,4),(7,2)] , find 3A-2Bdot

    Text Solution

    |

  9. Find non-zero values of x satisfying the matrix equation: x[(2x,2),(3,...

    Text Solution

    |

  10. Let A+2B=[(1,2,0),(6,-3,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,...

    Text Solution

    |

  11. If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2)...

    Text Solution

    |

  12. Prove that every square matrix can be uniquely expressed as the sum of...

    Text Solution

    |

  13. Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and 11 - n ...

    Text Solution

    |

  14. If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then AB and ...

    Text Solution

    |

  15. Find the value of x and y that satisfy the equations [(3,-2),(3,0),(2,...

    Text Solution

    |

  16. Find the values of x ,\ \ y\ ,\ z if the matrix A=[0 2y z x y-z x-y z]...

    Text Solution

    |

  17. If A=[costhetasintheta-sinthetacostheta], then prove that A^n=[cosnthe...

    Text Solution

    |

  18. If A=((p,q),(0,1)), then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(...

    Text Solution

    |

  19. Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove th...

    Text Solution

    |

  20. Show that the solutions of the equation [(x,y),(z,t)]^2=0 are[(x,y),(...

    Text Solution

    |