Determinant of a matrix (linear algebra)?

Question

when asked to give the determinant of a matrix in therms of a k (variable) what do i need to do.

i. e.

give the determinant of the matrix A in therms of x:


[ 2 -3 -1]
[-1 4 3]
[6 4x 2]

Answer 1

You can find the determinant of a 3x3 matrix by hand with the following handy formula:

the determinant of
[a,b,c]
[d,e,f]
[g,h,i]

is
a*(e*i - f*h) + b*(f*g - d*i) + c*(d*h - e*g)

Substituting your numbers in yields
2*(4*2 - 3*(3x)) + (-3)*(3*6 - (-1)*2) + (-1)*((-1)*(3x) - 4*6)

which works out to be
20 - 20x