Home
Class 12
MATHS
Verify that A=[[a,b],[c,d]] satisfies ...

Verify that `A=[[a,b],[c,d]]`
satisfies the equation `A^2-(a+d)A+(ad-bc) I=0` where `I` is the `2`x`2` unit matrix.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION SET

    USHA PUBLICATION|Exercise MODEL QUESTION SET|692 Videos

  • PREVIOUS YEAR QUESTION 2016

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |44 Videos

Similar Questions

Explore conceptually related problems

Show that the matrix A=[[2,3,],[1,2,]] satisfies the equation A^2-4A+I=O where I is a 2xx2 identity matrix and O is 2xx2 zero matrix.Using this equation.find A^-1 .

Verify that |P({a,b,c})|=2^3

Write the solution of the equation (d^2y)/(dx^2)=0

For the matrix A=[{:(3,1),(7,5):}] , find a and b such that A^(2)+aI=bA , where I is a 2xx2 identity matrix .

If A= [[ 3,-5,],[-4,2,]] ,show that A^2-5A-14I=O, where I is a unit matrix of Oder 2.

If the equation of x-axis is x/a=(y-d)/(b)=z/c , what is the value of a,b,c,d?

Show that A =((2,-3)(3,4)) satisfies equation x^2-6x+17=0 . Hence find A^-1 .

If A= [[4,2],[-1,1]] and I be the 2xx2 unit matrix find (A-2I)(A-3I)

USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

    Text Solution

    |

  2. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

    Text Solution

    |

  3. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

    Text Solution

    |

  4. Test differentiability and continuity of the following functions. |1...

    Text Solution

    |

  5. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

    Text Solution

    |

  6. Find dy/dx if y = x cot^(-1) (x/y)

    Text Solution

    |

  7. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

    Text Solution

    |

  8. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

    Text Solution

    |

  9. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

    Text Solution

    |

  10. int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)

    Text Solution

    |

  11. Find the area of the region bounded by y=6x-x^2x-axis and between ordi...

    Text Solution

    |

  12. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

    Text Solution

    |

  13. From a differential equation from the equation y=ae^(2x)+be^(-x) by el...

    Text Solution

    |

  14. Prove the following by vector method. An angle inscribed in a semi-cir...

    Text Solution

    |

  15. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

    Text Solution

    |

  16. If the sum of two unit vectors is a unit vector, show that the magnitu...

    Text Solution

    |

  17. Prove that the two lines whose direction cosines are connected by the ...

    Text Solution

    |

  18. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

    Text Solution

    |

  19. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

    Text Solution

    |

  20. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

    Text Solution

    |