Thread: Need help with: Making a Matrix Singular and Finding Determinates

Ok, i have been working on these problems for a bout an hour now and cant seem to find an answer.

1.)

Find all possible values of c that will make the matrix singluar

(c-1) -2 -3
(c-1) (c+1) -3
0 0 1


i used the formula (a11)(a22)(a33)-(a11)(a32)(a23)-(a12)(a21)(a33)+(a12)(a31)(a23)+(a13)(a21)(a32)-(a13)(a31)(a22)=0

solved it out to get c^2+2c-3=0
thus my roots are 3 and -1(but thats not the correct answer....)


2.)

Let A and B be 3X3 Matrices with det(A)=2 and det(B)=7

i know that for det(AB) you multiply the 2 but i need to find

det(2A)=?
det(3AB)=?
det(AB^-1)=?


3.)

If the determinate of a 4X4 matrix A is det(A)=9, and the matrix D is obtained from A by adding 3 times the third row to the second, determine det(D).



Any help is greatly appreciated
Thank you,
Drew

Hmm. For 1.), I get the determinant to be

the same as you. However, the solutions are the opposite signs you got.

For 2.), note that for an matrices and scalar you have





and, if is invertible, then



That should enable you to compute all the required quantities.

Thank you, Can anyone explain #3 for me please?

Originally Posted by Diggidy

[snip]
3.)

If the determinate of a 4X4 matrix A is det(A)=9, and the matrix D is obtained from A by adding 3 times the third row to the second, determine det(D).



Any help is greatly appreciated
Thank you,
Drew

There is a theorem you need to review regarding what happents to a determinant when you do this sort of elementary row operation. (Your class notes or textbook should list the various theorems for what happens to a determinant for diferent sorts of elementary row operations ....)