Answer:
130
Step-by-step explanation:
You want the determinant of the matrix ...
[tex]\left[\begin{array}{ccc}4&3&2\\-3&1&5\\-1&-4&3\end{array}\right][/tex]
One way to figure it is as the difference between the sum of products of the down-diagonals and the sum of products of the up-diagonals:
D = (4)(1)(3) +(3)(5)(-1) +(2)(-3)(-4) -(-1)(1)(2) -(-4)(5)(4) -(3)(-3)(3)
= 12 -15 +24 +2 +80 +27
D = 130
The determinant of the coefficient matrix is 130.
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Many scientific and graphing calculators and web sites can perform this calculation for you.
