Home
Class 12
MATHS
Without expanding the determinant at any...

Without expanding the determinant at any stage prove that ` |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}|` has a purely real value.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Determinants Exercise 7:|3 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DETERMINANTS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

Prove that the value of the determinant |{:(-7,,5+3i,,(2)/(3)-4i),(5-3i ,,8,,4+5i),((2)/(3) +4i,,4-5i,,9):}|" is real "

If a,b,c are real number, and D= |{:(,a,1+2i,3-5i),(,1-2i,b,-7-3i),(,3+5i,-7+3i,c):}| then show that D is purely real.

Simplify: (9+4i) ((3)/(2)-i) (9-4i)

Prove that [((3+2i)/(2-5i))+ ((3-2i)/(2+5i))] is rational

Find (2+4i)(3-2i)+(-3i)(5i)

Prove that the value of the determinant |-7 5+3i2/3-4i5-3i8 4+5i2/3+4i4-5fi9| is real.

Evaluate : (i) (2)/(3)-(4)/(5)

If z=|{:(3+2i,5-i,7-3i),(i,2i,-3i),(3-2i,5+i,7+3i):}|,"where "i=sqrt(-1),"then"

(2/(1-i) + 3/(1+i))((2+3i)/(4+5i)) is equal to

Find the modulus of the following using the property of modulus (3+2i)/(2-5i) + (3-2i)/(2+5i)

ARIHANT MATHS ENGLISH-DETERMINANTS -Exercise (Subjective Type Questions)
  1. Prove that |{:(b+c,c,b),(c,c+a,a),(b,a,a+b):}| = 4 abc

    Text Solution

    |

  2. Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

    Text Solution

    |

  3. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

    Text Solution

    |

  4. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

    Text Solution

    |

  5. Without expanding the determinant at any stage prove that |{:(-5,3+5i...

    Text Solution

    |

  6. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

    Text Solution

    |

  7. In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...

    Text Solution

    |

  8. The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...

    Text Solution

    |

  9. If y=(u)/(v), where u & v are functions of 'x' show that v^(3)(d^(2)y)...

    Text Solution

    |

  10. Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+al...

    Text Solution

    |

  11. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  12. (i) Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin...

    Text Solution

    |

  13. If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...

    Text Solution

    |

  14. If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x

    Text Solution

    |

  15. Show that in general there are three values of t for which the followi...

    Text Solution

    |

  16. Find dy/dx if y=13x-y^2

    Text Solution

    |

  17. If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...

    Text Solution

    |