Home
Class 12
MATHS
if the product of n matrices [(1,1),(0,1...

if the product of n matrices `[(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)]…[(1,n),(0,1)] is equal to the matrix [(1,378),(0,1)]` the value of n is equal to

A

`[(1,-12),(0,1)]`

B

`[(1,0),(12,1)]`

C

`[(1,-13),(0,1)]`

D

`[(1,0),(12,1)]`

Text Solution

Verified by Experts

The correct Answer is:
C
`[(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)].........[(1,n-1),(0,1)]=[(1,78),(0,1)]`
`rArr Sigma(n-1)=78=(n(n-1))/(2)=78rArr n(n-1)=156=12xx13 rArr n=13`
`rArr [(1,13),(0,1)]^(-1)=[(1,-13),(0,1)]`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 10| JEE -2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|6 Videos

  • JEE MAIN REVISION TEST - 13

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If A=[(1,2),(0,1)], then A^n= (A) [(1,2n),(0,1)] (B) [(2,n),(0,1)] (C) [(1,2n),(0,-1)] (D) [(1,n),(0,1)]

For what vlaue of n is |n-1|+1 equal to 0?

If A=[{:(0,1),(1,0):}] then A^(2) is equal to

Matrix [{:(1,0),(0,1):}] is :

if [{:(1,2,a),(0,1,4),(0,0,1):}]^n=[{:(1,18,2007),(0,1,36),(0,0,1):}] then find the value of n

If A=[{:(1,0,0),(0,1,0),(a,b,-1):}] then A^(2) is equal to

If A=[{:(1,0,0),(0,1,0),(a,b,-1):}] then A^(2) is equal to

If A=[{:(1,a),(0,1):}] then A^(n) (where n in N ) is equal to

Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)] , then find A^(-1) .

If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdotcdot[{:(1, n-1), (0,1):}] = [{:(1, 78), (0,1):}] , then the inverse of [{:(1, n), (0,1):}] is

VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 12 -MATHEMATICS
  1. If the line (x-1)/(2)=(y+1)/(3)=(z-2)/(4) meets the plane, x+2y+3z=15 ...

    Text Solution

    |

  2. If the function f: R -{1,-1} to A definded by f(x)=(x^(2))/(1-x^(2)), ...

    Text Solution

    |

  3. if the product of n matrices [(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)]…[...

    Text Solution

    |

  4. If f(x) is a non-zero polynomial of degree four, having loca extreme p...

    Text Solution

    |

  5. If the line y = mx + 7 sqrt(3) is normal to the hyperbola (x^(2))/(...

    Text Solution

    |

  6. A plane passes through the point (0,-1,0) and (0,0,1) and makes an ang...

    Text Solution

    |

  7. Let hat(alpha) = 3 hat(i)+hat(j) and hat(beta)= 2 hat(i)-hat(j)+3hat...

    Text Solution

    |

  8. Let the sum of the first n terms of a non-constant A.P., a(1), a(2), a...

    Text Solution

    |

  9. If the function f defined on (pi/6,pi/3) by {{:((sqrt2 cos x -1)/(cot ...

    Text Solution

    |

  10. All the points in the set S={(alpha+i)/(alpha-i):alpha in R } (i= sqrt...

    Text Solution

    |

  11. If the fourth term in the binomial expansin of ((2)/(x) + x^(log(8) x)...

    Text Solution

    |

  12. Let f(x) = 15 -|x-10|, x in R. Then, the set of all values of x, at w...

    Text Solution

    |

  13. Let p, q in R. If 2- sqrt3 is a root of the quadratic equation, x^(2...

    Text Solution

    |

  14. The integral int sec^(2//3)x cosec^(4//3)x dx is equal to : (Here C ...

    Text Solution

    |

  15. If the tangent to the curve, y=x^(3)+ax-b at the point (1, -5) is perp...

    Text Solution

    |

  16. If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axe...

    Text Solution

    |

  17. Four persons can hit a target correctly with probabilities (1)/(2),(1)...

    Text Solution

    |

  18. The area (in sq. units) of the region {(x,y) in R^(2) : x^(2) le y le ...

    Text Solution

    |

  19. Find the natural number a for which sum(k=1)^nf(a+k)=16(2^n-1), where...

    Text Solution

    |

  20. Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

    Text Solution

    |