WEBVTT
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Find the value of the determinant of this three-by-three matrix.
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Remember, the determinant of a three-by-three matrix π, π, π, π, π, π, π, β, π shown is equal to π multiplied by ππ minus πβ minus π multiplied by ππ minus ππ plus π multiplied by πβ minus ππ.
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Another way to think about this is to look at each of the elements on the top right.
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We multiply the first element on the top row by the determinant of the two-by-two matrix thatβs not in πs row or column.
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And to find the determinant of a two-by-two matrix, we multiply the top left and bottom right element.
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And then we subtract the product of the top right and bottom left element.
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We then subtract π multiplied by the two-by-two matrix thatβs not in πs row or column.
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And finally, we add π multiplied by the determinant of the two-by-two matrix thatβs not in πs row or column.
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Thatβs negative two multiplied by one multiplied by negative five minus eight multiplied by zero.
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Then, we subtract five multiplied by five multiplied by negative five minus eight multiplied by zero.
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And finally, we add negative eight multiplied by five multiplied by zero minus one multiplied by zero.
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We have quite a lot of products which give us an answer of zero here.
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So actually, our expression for the determinant of our matrix simplifies to negative two multiplied by negative five minus five multiplied by negative 25.
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Negative two multiplied by negative five is 10.
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And negative five multiplied by negative 25 is positive 125.
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And we found the determinant of our matrix.
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Itβs 135.