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)

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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)

MIT 18.06 Linear Algebra, Spring 2010
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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. \[\left[\begin{matrix}1 & 2 &0\\ 1& 8&3\\0&10&5\end{matrix}\right]\]
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.
I got it! x + a + 0 = 0 2x + 8 + yb = 0 0 + 5y + 3 = 0 Therefore, 3b + 10a = 40

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