Home
Class 12
MATHS
If A=[{:(-1,2),(3,1):}], find f(A), wher...

If `A=[{:(-1,2),(3,1):}]`, find f(A), where `f(x)=x^(2)-2x+3.`

Text Solution

AI Generated Solution

To solve the problem, we need to find \( f(A) \) where \( A = \begin{pmatrix} -1 & 2 \\ 3 & 1 \end{pmatrix} \) and \( f(x) = x^2 - 2x + 3 \). ### Step 1: Substitute \( A \) into \( f(x) \) We start by substituting \( A \) into the function \( f(x) \): \[ f(A) = A^2 - 2A + 3I \] where \( I \) is the identity matrix. ...
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5D|15 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5E|15 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5B|16 Videos

  • LINEAR PROGRAMMING

    RS AGGARWAL|Exercise SECTION D|6 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Objective Questions Ii|56 Videos

Similar Questions

Explore conceptually related problems

If A=[(3,1),(-1,2)] , then find f (A), where f(x)=x^(2)-5x+7 .

If A = [[-4,1],[3,2]] find f(A) if f(x) =x^2 - 2x+3

If A=[{:(1,2),(4,-3):}] and f(x)=2x^(3)+4x+5 , find f(A).

Find (lim)_(x rarr1)f(x), where f(x)=[x^(2)-1,x 1

If f(x-1)=f(x+1) , where f(x)=x^2-2x+3 , then: x=

Find 'a' if f^(')(a)=0 , where f(x)=x^(3)-3x^(2)+3x-1

Find 1) gof and 2) fog where f(x)=x-2g(x)=x^(2)+3x+1

Evaluate: lim_(x rarr 1) (f(x)-f(1))/(x-1), "where" f(x) = x^(2)-2x .

If f'(x)=3x^(2)-(2)/(x^(3)) and f(1)=0, find f(x)

If f'(x)=x-3/x^2,f(1)=11/2 , find f(x).

RS AGGARWAL-MATRICES-Exercise 5C
  1. Show that the matrix A=[2 3 1 2] satisfies the equation A^3-4A^2+A=O .

    Text Solution

    |

  2. If A A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

    Text Solution

    |

  3. If A=[{:(-1,2),(3,1):}], find f(A), where f(x)=x^(2)-2x+3.

    Text Solution

    |

  4. If A=[{:(1,2),(4,-3):}] and f(x)=2x^(3)+4x+5, find f(A).

    Text Solution

    |

  5. Find the values of x and y for which [{:(2,-3),(1," "1):}][{:(x),(y)...

    Text Solution

    |

  6. Solve for x and y, when [{:(3,-4),(1," "2):}][{:(x),(y):}]=[{:(3),(1...

    Text Solution

    |

  7. If A=[{:(3,1),(7,5):}], find x and y such that A^(2)+xI=yA.

    Text Solution

    |

  8. Solve system of linear equations, using matrix method, x y" "+" "2...

    Text Solution

    |

  9. Find the matrix A such that [[5-7,],[-2,3]]A=[[-16,-6],[7,2]].

    Text Solution

    |

  10. Find the matrix A such that A.[{:(2,3),(4,5):}]=[{:(0,-4),(10," "3):}]...

    Text Solution

    |

  11. If A=[{:(1,-1),(2,-1):}],B=[{:(a,-1),(b,-1):}]" and "(A+B)^(2)=(A^(2)+...

    Text Solution

    |

  12. If F(x)=[{:(cosx,-sinx,0),(six,cosx,0),(0,0,1):}], show that F(x).F(y)...

    Text Solution

    |

  13. If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}], show that A^(2)=[...

    Text Solution

    |

  14. If [1" "x" "1][{:(1,2,3),(4,5,6),(3,2,5):}][{:(" "1),(-2),(" "3):}]=O,...

    Text Solution

    |

  15. If [[x, 4, 1]] [[2,-1,2] , [1,0,2] , [0,2,-4]] [[x], [4], [1]]=0 then ...

    Text Solution

    |

  16. Find the values of a and b which [{:(a,b),(-a,2b):}][{:(" "2),(-1):}...

    Text Solution

    |

  17. If A=[{:(" "3," "4),(-4,-3):}], find f(A), where f(x)=x^(2)-5x+7.

    Text Solution

    |

  18. If A=[{:(1,1),(0,1):}], prove that A=[{:(1,n),(0,1):}] for all n inN.

    Text Solution

    |

  19. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\...

    Text Solution

    |

  20. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

    Text Solution

    |