Question

Which numbers a and b make the matrix singular:
\left[\begin{matrix}1 & 2 &0\\ a & 8&3\\0&b&5end{matrix}\right]
(Copy & Past the code for the matrix to the reply to see the matrix)

Answer 1

For a matrix to be singular det A = 0 (A is some square matrix). In your case a= 1 and b= 10 is one of the solutions.
\[\left[\begin{matrix}1 & 2 &0\\ 1& 8&3\\0&10&5\end{matrix}\right]\]

Answer 2

This is question 16, from chapter/topic 1.5 in Linear Algebra and is Applications, by professor Strang. I should have put the solution, since it is at the end of the book. Because I wanted to see how this problem can be solved. Anyways, the answer professor gives is not a point (a, b), a and b that makes singular this matrix
\[\left[\begin{matrix}1 & 2 &0\\ a & 8&3\\0&b&5\end{matrix}\right]\]
is a line:\[3b + 10a = 40\]
I just don't know how to get to that answer.

Answer 3

I got it!
x + a + 0 = 0
2x + 8 + yb = 0
0 + 5y + 3 = 0
Therefore,
3b + 10a = 40