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.

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 3

    MODERN PUBLICATION|Exercise PROBLEM|63 Videos
  • TEST PAPER 5

    MODERN PUBLICATION|Exercise PROBLEM|41 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)

MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. An animal feed company must produce 200kg of a mixture consisting of i...

    Text Solution

    |

  2. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

    Text Solution

    |

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

    Text Solution

    |

  4. If A+B+C = pi, prove that [[sin^2A,cotA,1],[sin^2B,cotB,1],[sin^2C,c...

    Text Solution

    |

  5. If A=[[1,2,3],[3,-2,1],[4,2,1]]"show that"A^3-23A-40I=0

    Text Solution

    |

  6. Show that (a+1) is a factor of abs([(a+1),2,3],[1,a+1,3],[3,-6,a+1])

    Text Solution

    |

  7. Find the dy/dx when x = a[cos t + log tan (t//2)], y = a sin t

    Text Solution

    |

  8. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

    Text Solution

    |

  9. inttan^-1(secx+tanx)dx

    Text Solution

    |

  10. If the magnitude of the difference of two unit vectors is sqrt3 then f...

    Text Solution

    |

  11. Find the equation of the plane if the point (5,-3,4) is the foot of th...

    Text Solution

    |

  12. Proved that the line (x-1)/2=(y+2)/(-3)=(z-3)/1 lies on the plane 7x+5...

    Text Solution

    |

  13. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

    Text Solution

    |

  14. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

    Text Solution

    |

  15. If A=[{:(1,2,0),(-2,-1,-2),(0,-1,1):}] then find A^-1 Using A^-1 solv...

    Text Solution

    |

  16. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

    Text Solution

    |

  17. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

    Text Solution

    |

  18. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

    Text Solution

    |

  19. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

    Text Solution

    |

  20. Find the area enclosed by y^2=x^3,x=0,y=1

    Text Solution

    |