# Solving for X in a matrix

• Jun 23rd 2012, 07:16 AM
astuart
Solving for X in a matrix
I don't know where I should be going when solving for an unknown in a matrix.

My question is "Find the value of x for which A does not have an inverse".

A=
(1 3)
(x 2)

The statement 'A does not have an inverse' throws me off - does this mean there is no inverse? I know how to find the inverse of a matrix, but don't know how to solve for x. Is finding the inverse the goal of the exercise?

Cheers
• Jun 23rd 2012, 07:32 AM
mfb
Re: Solving for X in a matrix
Quote:

does this mean there is no inverse?
With a specific value of x, there is no inverse, right.
You can try to invert the matrix. At some point, you will see that you have to divide by some expression with x inside. If this expression is 0, the operation is not valid, and you cannot invert the matrix.

Simple example:

B=
(1 0)
(0 x)
With $x \neq 0$, it is easy to invert. But if you set x=0, there is no inverse matrix.
• Jun 23rd 2012, 07:39 AM
Plato
Re: Solving for X in a matrix
Quote:

Originally Posted by astuart
I don't know where I should be going when solving for an unknown in a matrix.

My question is "Find the value of x for which A does not have an inverse".

A=
(1 3)
(x 2)

The statement 'A does not have an inverse' throws me off - does this mean there is no inverse? I know how to find the inverse of a matrix, but don't know how to solve for x. Is finding the inverse the goal of the exercise?

Cheers

The matrix $\left( {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right)$ has no inverse if $ad-bc=0$
• Jun 23rd 2012, 07:47 AM
astuart
Re: Solving for X in a matrix
Great, that makes sence now. 12:30am math homework doesn't go down to well..

(1 3)
(x 2)

1x2 - 3x(x) = 0
2 - 3x = 0
-3x = -2
x = (2/3)

1x2 - 3(2/3) = 0
2 - 2 = 0

Cheers guys.