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Hi, in this question, we have learned that a is a 3x3 matrix with determinant of a equals minus 2.
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We need to evaluate the following.
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For part a, modulus 3a i .e.
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Determinant of 3a.
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We know that the formula determinant of ka equals k power n determinant of a.
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So, this is m cross n matrix.
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N equals 3.
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So, that modulus of 3a can be written as 3 cube determinant of a which is equal to 3 cube is 27 into determinant of a is minus 2 which is equal to minus 54.
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Next, we have to evaluate determinant of 2a a transpose.
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We can write it as determinant of 2a a transpose equals 2 power n determinant of a a transpose.
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And here determinant of a a transpose can be written as determinant of a into a transpose.
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And we know that determinant of a equals determinant of a transpose.
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So, that determinant of a a transpose can be written as minus 2 into minus 2 which is equal to 4...