Show without computation that the following determinate is equal to zero?

We are given the matrix:

| 0 2 -3 |

| -2 0 4 |

| 3 -4 0 |

And we are asked to prove that the determinate will be 0, without actually solving for the determinate step-by-step. How do we do this? Thank you! :)

2 Answers

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  • Elmyr
    Lv 7
    1 decade ago
    Favorite Answer

    Umm...isn't that 24?

    d = (aei + bfg + cdh) - (gec + hfa + idb)

    aei = 0

    bfg = 2 * 4 * 3 = 24

    cdh = 0

    gec = 0

    hfa = 0

    idb = 0

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  • 1 decade ago

    All the entries along the main diagonal are 0. This is a signal that the determinant will be 0. If you want proof, algebraically find the determinant. You will see that the other numbers are multiplied by 0 somewhere.

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