Home
Class 12
MATHS
Suppose a1, a2, are real numbers, with ...

Suppose `a_1, a_2, ` are real numbers, with `a_1!=0.` If `a_1, a_2,a_3, ` are in A.P., then (a)`A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)]` is singular (where `i=sqrt(-1)`) (b)The system of equations `a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9z=0` has infinite number of solutions. (c)`B=[(a_1,i a_2),(ia_2,a_1)]` is non-singular (d)none of these

Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If a_r=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

If a_r=(cos2rpi+isin2rpi)^((1)/(9)) , then the value of |{:(a_1,a_2,a_3),(a_4,a_5,a_6),(a_7,a_8,a_9):}| .

If a_1,a_2,a3,...,a_n are in A.P then show that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n)

If a_1, a_2, a_3,54,a_6,a_7, a_8, a_9 are in H.P., and D=|[a_1,a_2,a_3],[5, 4,a_6],[a_7,a_8,a_9]| , then the value of [D]i sw h e r e[dot] represents the greatest integer function

The total number of infections (one-one into mappings) from {a_1,a_2,a_3,a_4} to {b_1,b_2,b_3,b_4,b_5,b_6,b_7} is

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

A function is defined as f:{a_1,a_2,a_3,a_4,a_5,a_6}rarr{b_1,b_2,b_3} then number of functions in which f(a_i)neb_i is divisible by

If a_1 and a_2 are two non-collinear unit vectors and if |a_1+a_2|=sqrt(3) , then the value of (a_1-a_2)*(2a_1+a_2) is

If a_1,a_2,a_3...a_n are in HP and f(k)=sum_(r=1)^na_r-a_k, then a_1/(f(1)),a_2/(f(2)),a_3/(f(3)),......a_n/(f(n)) are in

If the lines a_1x+b_1y+1=0,a_2x+b_2y+1=0 and a_3x+b_3y+1=0 are concurrent, show that the point (a_1, b_1),(a_1, b_2) and (a_3, b_3) are collinear.

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If A is an invertible matrix, then (a d jdotA^(-1)) is equal to a.[a ...

    Text Solution

    |

  2. If A=(a(i j))(nxxn) and f is a function, we define f(A)=((f(a(i j))))(...

    Text Solution

    |

  3. Suppose a1, a2, are real numbers, with a1!=0. If a1, a2,a3, are in A...

    Text Solution

    |

  4. If A,B,C are three square matrices of the same order, then A B=A C =>...

    Text Solution

    |

  5. Let A=[1 0 1 1] . Then which of following is not true? (lim)(nvecoo)1/...

    Text Solution

    |

  6. If alpha,beta,gamma are real numbers, then without expanding at any...

    Text Solution

    |

  7. The matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is (A) idempotent mat...

    Text Solution

    |

  8. If P (E) = 0.05, what is the probability of ‘not E’?

    Text Solution

    |

  9. If A=[[a,b],[c,d]] (where b c!=0 ) satisfies the equations x^2+k=0,t h...

    Text Solution

    |

  10. If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to a.B A ...

    Text Solution

    |

  11. Given the matrix A=[[x,3,2],[1,y,4],[2,2,z]]. If xyz=60 and 8x+4y+3z=2...

    Text Solution

    |

  12. Let A +2B=[[1, 2, 0],[ 6,-3, 3],[-5, 3, 1] ] and 2A-B=[[2,-1, 5 ],[2,-...

    Text Solution

    |

  13. Which of the following in an orthogonal matrix

    Text Solution

    |

  14. If k in Ro then det{adj(k In)} is equal to (A) K^(n-1) (B) K^((n-1)...

    Text Solution

    |

  15. If A1, A2, , A(2n-1) are n skew-symmetric matrices of same order, th...

    Text Solution

    |

  16. Let A=[[1 ,2 ,3],[ 2, 0, 5],[ 0 ,2 ,1]] and B=[[0],[-3],[1]] . Which ...

    Text Solution

    |

  17. Column I, Column II If |A|=2,t h e n|2A^(-1)=(w h e r eA is of orde...

    Text Solution

    |

  18. A=[[0 ,1],[ 3 ,0]]a n d(A^8+A^6+A^4+A^2+I) V=[[0] ,[11]](w h e r e I i...

    Text Solution

    |

  19. Show that every square matrix A can be uniquely expressed as P+i Q ,wh...

    Text Solution

    |

  20. Express A as the sum of a Hermitian and a skew-Hermitian matrix, where...

    Text Solution

    |