Matrices Question

The_Gatsby

Can anybody help me with this question?



I know how to get the determinant but I'm not sure which of the 2 matrices I'm supposed to use for the question.

thanks for any help

Michael Collins

The cofactors in the 2nd matrix are obtained by eliminating the row and column of the position in question from the first matrix, and obtaining the determinant of the reduced matrix left over (and then adjusting sign accordingly). For example, the first entry in the 2nd matrix (the matrix of cofactors) is -16. This is obtained by eliminating the first row and column from the first matrix, now you are left with the following

[latex] a_{11} = +{\left|\matrix{-1 & 2 \cr 6 & 4 \cr} \right|} = -16. [/latex]

Similarly for the second entry in the matrix of cofactors

[latex] a_{12} = -{\left|\matrix{4 & 2 \cr -2 & 4 \cr} \right|} = -20. [/latex]

Note the minus above. This alternates between plus and minus for each cofactor - if you like you can use the subscript to tell you if there needs to be an extra minus added, if the indices add to an odd number e.g. [latex] a_{12} \to [/latex] 1+2=3 above, then there needs to be an extra minus.

This should allow you to figure out p, q and r. Come back with their values when you have them, the inverse part is very easy from that point on.

The_Gatsby

Thanks very much, just worked it out and am delighted as this question will give me full marks in an exam tomorrow! Thanks a lot for the reply