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

Suppose `a_1, a_, ` 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_9=0 has infinite number of solutions. (c)`B=[(a_1,i a_2),(ia_2,a_1)]` is non-singular (d)none of these

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, ia_2),(ia_2,a_1)]` is nonsingular

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE MAIN ARCHIVE|92 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

  • JEE MAIN REVISON TEST-23

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

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

Similar Questions

Explore conceptually related problems

|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 then the system of equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0, a_3x+b_3y+c_3z=0 has

If a_r=(cos2rpi+i sin 2rpi)^(1//9) , then prove that |[a_1,a_2,a_3],[a_4,a_5,a_6],[a_7,a_8,a_9]|=0 .

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1, a_2, ,a_n are in H.P., then (a_1)/(a_2+a_3++a_n),(a_2)/(a_1+a_3++a_n), ,(a_n)/(a_1+a_2++a_(n-1)) are in a. A.P b. G.P. c. H.P. d. none of these

a_1,a_2, a_3, ,a_n are in A.P. and a_1+a_3+a_5+a_7+a_9=20 then a_5 is 2 2. 7 3. 3 4. 4 5. 5

Evaluate: /_\ |[1+a_1, a_2, a_3],[a_1, 1+a_2, a_3],[a_1, a_2, 1+a_3]|

Evaluate: /_\ |[1+a_1, a_2, a_3],[a_1, 1+a_2, a_3],[a_1, a_2, 1+a_3]|

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

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -LEVEL 2
  1. Which of the following statements is/are true about square matrix A or...

    Text Solution

    |

  2. If A, B, and C are three square matrices of the same order, then AB=AC...

    Text Solution

    |

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

    Text Solution

    |

  4. Let A=[(1,0),(1,1)] . Then which of the following is not true ?

    Text Solution

    |

  5. If C is skew-symmetric matrix of order n and X isnxx1 column matrix, t...

    Text Solution

    |

  6. If S=[(0,1,1),(1,0,1),(1,1,0)]a n dA=[(b+c,c+a,b-c),(c-b,c+b, a-b),(b-...

    Text Solution

    |

  7. If A B=A and B A=B , then show that A^2=A , B^2=B .

    Text Solution

    |

  8. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

    Text Solution

    |

  9. Let A=a0 be a matrix of order 3, where a(i j)=x ; ifi=j ,x in R, 1 if...

    Text Solution

    |

  10. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

    Text Solution

    |

  11. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

    Text Solution

    |

  12. Let A=[a("ij")](3xx3) be a matrix such that A A^(T)=4I and a("ij")+2c(...

    Text Solution

    |

  13. Let A and B be two nonsingular square matrices, A^(T) and B^(T) are th...

    Text Solution

    |

  14. If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsi...

    Text Solution

    |

  15. If A^(-1)=[(sin^(2)alpha, 0, 0),(0, sin^(2)beta,0),(0, 0,sin^(2)gamma)...

    Text Solution

    |

  16. A is even ordered non singular symmetric matrix and B is even ordered ...

    Text Solution

    |

  17. If P is a 3xx3 matrix such that P^(T) = 2 P + I , where P^(T) is the...

    Text Solution

    |

  18. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. Suppose a, b, c, in R and abc = 1, if A = [[3a, b, c ],[b, 3c, a ],[c...

    Text Solution

    |