Question

What is the determinant of the coefficient matrix of the system {4x+3y+2z=0 -3x+y+5z=0 -x-4y+3z=0

Answer 1

130

Explanation:

You want the determinant of the matrix ...

`\left[\begin{array}{ccc}4&3&2\\-3&1&5\\-1&-4&3\end{array}\right]`

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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