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Question 568945: whta is the determinant of
2 3
3 2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! This is a 2-by-2 determinant, meaning that it has two rows and two columns.
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The value of a 2-by-2 determinant is found by multiplying along the diagonals.
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The first diagonal to multiply along is the one that goes from the upper left corner to the lower right corner. This diagonal multiplication gives you the product of 2 times 2, which, of course, equals +4.
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The second diagonal to multiply along is the one that goes from the upper right corner to the lower left corner. This diagonal multiplication gives you the product of 3 times 3 which is +9.
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The final step is to note the product of the first diagonal multiplication (down and to the right - in this problem +4) and subtract from it the product of the second diagonal (down and to the left - in this problem +9).
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So the value of this determinant is given by:
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+4 - (+9) = 4 - 9 = -5
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The answer to this problem is that the value of the given determinant is -5.
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In summary, to get the value of a 2-by-2 determinant, first find the product obtained by multiplying down and to the right and second, subtract from that the product obtained by multiplying down and to the left.
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I hope this helps you to understand the rules for evaluating 2-by-2 determinants.
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