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Q . THE PROPERTIES OF DETERMINANTS

An n×nmatrix A is called skew-symmetric if At=−A. Show that if Ais skew-symmetric and nis an

odd positive integer, then Ais not invertible.

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Q . CRAMER’S RULE, VOLUME, AND LINEAR TRANSFORMATIONS

Solve the linear system using Cramer’s Rule:

x1+ 2x2+ 3x3= 6

2x2+ 3x3= 5

x3= 1

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