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Prove that the value of the determinan...

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 "`

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

Whitout expanding the determinat 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.

Knowledge Check

  • If z = |{:(-5,3+4i,5-7i),(3-4i,6,8+7i),(5+7i,8-7i,9):}| , then z is

    A
    purely real
    B
    purely imaginary
    C
    a + ib, where a `ne` 0, `b ne 0 `
    D
    a + ib, where b = 4

  • If Delta=|(-1,2+3i,5-4i),(2-3i,8,1-i),(5+4i,1+i,3)| then Delta is

    A
    purely real
    B
    purely imaginary
    C
    complex
    D
    0

  • If A A={:(23,1+i,-i),(-i,-3i,4-5i),(i,4+5i,17):} then det (A) is

    A
    complex number with positive real part
    B
    complex number with negative imaginary part
    C
    pure imaginary
    D
    real

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