Week7 - ECON 117 Mathematical Economics Spring 2008 Week 7...

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ECON 117 Spring 2008 Mathematical Economics Week 7 3.4 The Properties of Determinant 1. = AA 2. If is obtained from by interchanging any two rows (or columns) of , then B A A =− BA Ex) 121 212 2 1 2 1 2 1 011 ⎡⎤ ⎢⎥ == ⎣⎦ AB 3. If has two identical rows (or columns), then A 0 = A Ex) 1 2 1 = A Page 1 of 4
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ECON 117 Spring 2008 Mathematical Economics 4. 11 1 1 1 1 n ii jj nn aa ⎡⎤ ⎢⎥ = ⎣⎦ A "" ## n n n Then (expanding by a wrong row) 11 2 2 0 j i j i jn in aC ++ = " 5. is obtained from by adding a multiple of one row (or column) to another row (or column), then B A = BA Page 2 of 4
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ECON 117 Spring 2008 Mathematical Economics 6. is obtained from by multiplying one row (or column) of by B A A λ . Then, =⋅ BA 7. If the rows (or columns) of
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This note was uploaded on 09/15/2008 for the course ECON 324 taught by Professor Kim during the Spring '08 term at HKUST.

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Week7 - ECON 117 Mathematical Economics Spring 2008 Week 7...

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