- #1

- 86

- 0

## Homework Statement

Find the values of a and b such that the equations:

3x + ay = 2 and -6x + 4y = b

have i) an infinite set of solutions ii) no solutions

## The Attempt at a Solution

[itex]\begin{pmatrix}

3 & a \\

-6 & 4

\end{pmatrix} * \begin{pmatrix}

x\\

y

\end{pmatrix}

= \begin{pmatrix}

2\\

b

\end{pmatrix}[/itex]

[itex]

\begin{pmatrix}

x\\

y

\end{pmatrix}

=

\begin{pmatrix}

3 & a \\

-6 & 4

\end{pmatrix}^{-1} *

\begin{pmatrix}

2\\

b

\end{pmatrix}

[/itex]

[itex]

\begin{pmatrix}

x\\

y

\end{pmatrix}

=

\tfrac{1}{12+6a} *

\begin{pmatrix}

4 & -a \\

6 & 3

\end{pmatrix} *

\begin{pmatrix}

2\\

b

\end{pmatrix}

[/itex]

I think that when the matrix is singular, then it does not have ONE solution (infinite OR no solution). So when a = -2 then it has infinite OR no solution. But what about b, how do I figure out the value for b?

Thanks