SOLUTION: Let B =( matrix (3,3, 1,2,3, 2,k-3,3, 3,4,k-4 ) ) a)Find det(B) in terms of k; b)For what value(s) of k are the column vectors of B linearly dependent c)For k = 0, find

Question 1006746: Let B =(
matrix (3,3,
1,2,3,
2,k-3,3,
3,4,k-4
)
)
a)Find det(B) in terms of k;
b)For what value(s) of k are the column vectors of B linearly dependent
c)For k = 0, find det(B) and det (-1/2B^tBB^-1) .

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

I'll do the first part, part (a), to get you started

I'm using the method shown below

(Image Source: Wikipedia)

Using that method, we can say

Let's compute the sub-determinants (the determinants of the 2x2 submatrices)

----------------------------------------------------

----------------------------------------------------

Now let's return to the determinant of the 3x3 matrix.

Make the proper substitutions (see the sub-determinants above)

Distribute

Combine like terms. This is the final answer for part (a)
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