Question 1055331
.
Find the value(s)of b for which Z = 

6   −b    −4
b    0     1
1   −2     1

 is singular

i worked it but not sure of the answer,
please show me the steps to get the answer.
thank you
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Z = {{{(matrix(3,3, 6,-b,-4,  b,0,1,  1,-2,1))}}}.


det(Z) = [6*0*1 + (-b)*1*1 + b*(-2)*(-4)] - [1*0*(-4) + b*(-b)*1 + 6*(-2)*1] = 

          0 - b + 8b + 0 + b^2 + 12 = b^2 + 7b + 12.

The matrix is singular if and only if det(Z) = 0, i.e.

b^2 + 7b + 12 = 0.

Factor the polynomial in the left side:

(b-3)*(b-4) = 0.

The roots are b = 3  and  b = 4.

The matrix Z is singular if and only if b = 3  or  b = 4.
</pre>

On calculating determinants of 3x3 matrices see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Matrices-and-determiminant/Determinant-of-a-3x3-matrix.lesson>Determinant of a 3x3 matrix</A> 

in this site.



Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
&nbsp;&nbsp;&nbsp;&nbsp; "<U>3x3-Matrices, determinants, Cramer's rule for systems in three unknowns</U>"