Home
Class 12
MATHS
Let f(x)=x^2-5x+6. Find f(A), if A=[[2, ...

Let `f(x)=x^2-5x+6`. Find `f(A)`, if `A=[[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]]`

Text Solution

Verified by Experts

Given,
`A=[[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]]`

`f(x)=x^2-5x+6`
`f(A)=A^2-5A+6`
`f(A)=[[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]][[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]]-5[[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]]+6I`

`f(A)=[[4+0+1, 0+0-1 ,2+0+0],[4+2+3, 0+1-3, 2+3+0],[ 2-2+0,0-1+0, 1-3+0]]-[[10, 0 ,5],[10, 5, 15],[ 5,-5, 0]]+6[[1,0,0],[0,1,0],[0,0,1]]`

`f(A)=[[5, -1 ,2],[9, -2, 5],[0,-1, -2]]-[[10, 0 ,5],[10, 5, 15],[ 5,-5, 0]]+[[6,0,0],[0,6,0],[0,0,6]]`

`f(A)=[[5-10+6, -1+0+0 ,2-5+0],[9-10+0, -2-5+6, 5-15+0],[0-5+0,-1+5+0, -2+0+6]]`

...
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

If f(x)=x^2-5x+6. Find f(A),if A=[(2,0,1),(2,1,3),(1,-1,0)] .

If f(x)=x^2-2x , find f(A), where A=[(0, 1, 2),( 4 ,5, 0 ),(0, 2 ,3)] .

Let f(x)=x^(3)/3-x^(2)/2+x-16 . Find f^(')(0), f^(')(-1) .

If f(x)=x^(2)+3x-5, find f(0),f(1) and f((1)/(2))

Let f : R rarr given by f(x) = 3x^(2) + 5x + 1 . Find f(0), f(1), f(2).

If f'(x)=4x^3-3x^2+2x+k and f(0)=1, f(1)=4 find f(x)

Let f(x)=int(1)/((1+x^(2))^(3//2))dx and f(0)=0 then f(1)=

Find f(f(x)) if f(x)=x+1;0<=x<=1 and 1-x;1

Let g(x)=2f((x)/(2))+f(1-x) and f'(x)<0 in 0<=x<=1 then g(x)

Let f(x)=x^(2)-x-3=0 .Given f(a)=0 ; then the value of (a^(3)+1)/(a^(5)-a^(4)-a^(3)+a^(2)) equals

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A= [[0, 1],[-1, 0]], find xand y such that (x I+y A)^2=A

    Text Solution

    |

  2. If [(2,-1),(1,0),(-3,4)]A=[(-1,-8,-10),(1,-2,-5),(9,22,15)], find A.

    Text Solution

    |

  3. Let f(x)=x^2-5x+6. Find f(A), if A=[[2, 0 ,1],[2, 1, 3],[ 1,-1, 0]]

    Text Solution

    |

  4. If A and B are symmetric matrices of the same order, write whether AB-...

    Text Solution

    |

  5. If A is a square matrix such that A^2=A ,then (I+A)^3-7A is equal to

    Text Solution

    |

  6. If A is a square matrix such that A^2=A , then write the value of 7A-(...

    Text Solution

    |

  7. Construct a 3xx4 matrix A=[a(i j)] whose elements are given by (i)a...

    Text Solution

    |

  8. If [x-y2x+z2x-y3z+w]=[-1 5 0 13] , find x ,\ y ,\ z ,\ wdot

    Text Solution

    |

  9. Find the values of x ,\ y ,\ z and a which satisfy the matrix equ...

    Text Solution

    |

  10. A matrix has 12 elements. What are the possible orders it can have?

    Text Solution

    |

  11. If A=[a(i j)] is a matrix given by A=[a(i j)]=[4 5 21\ \ -2 7 15\ \ 1 ...

    Text Solution

    |

  12. A matrix has 12 elements. What are the possible orders it can have?

    Text Solution

    |

  13. Construct a 2xx2 matrix A=[a(i j)] whose elements are given by a(i ...

    Text Solution

    |

  14. Construct a 2xx3 matrix A=[a(i j)] whose elements are given by a(i ...

    Text Solution

    |

  15. Construct a 3xx2 matrix A=[a(i j)] whose elements are given by a(i ...

    Text Solution

    |

  16. Find x ,\ y ,\ z and w such that [(x-y,2z+w),(2x-y,2x+w)]=[(5, 3 ),(...

    Text Solution

    |

  17. Consider the following information regarding the number of men and ...

    Text Solution

    |

  18. Find Value of K, for which A =[(K, 8),( 4, 2K)] is a singular matrix i...

    Text Solution

    |

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

    Text Solution

    |

  20. If a matrix has 8 elements, what are the possible orders it can hav...

    Text Solution

    |