{ 3 2 } x { a b } = { 1 0 }

{ 1 -1 } { c d } { 0 1 }

So, what is:

{ a b } = { 1 0 } x Inv. { 3 2 }

{ c d } { 0 1 } { 1 -1 }

can any help me figure it out this matrix

its do to with "inverse"

thanks in advance

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- Feb 15th 2009, 05:55 AMkarimwahabmatrix multiplication
{ 3 2 } x { a b } = { 1 0 }

{ 1 -1 } { c d } { 0 1 }

So, what is:

{ a b } = { 1 0 } x Inv. { 3 2 }

{ c d } { 0 1 } { 1 -1 }

can any help me figure it out this matrix

its do to with "inverse"

thanks in advance - Feb 15th 2009, 08:07 PMCaptainBlack
- Feb 16th 2009, 08:21 AMGrandadInverse of a 2x2 matrix
Hello karimwahabI'm not entirely sure what you mean by the part in red, but the first part is clear enough. It is:

$\displaystyle \begin{pmatrix}3&2\\1&-1 \end{pmatrix}\begin{pmatrix}a&b\\c&d \end{pmatrix}=\begin{pmatrix}1&0\\0&1 \end{pmatrix}$

Now the matrix $\displaystyle \begin{pmatrix}1&0\\0&1 \end{pmatrix}$ is called the*Identity Matrix*, usually denoted by $\displaystyle I$. This matrix has the special property that when any other 2x2 matrix is multiplied by it (either on the left or the right) then that matrix is unchanged - it keeps its*identity*. In other words, for any matrix $\displaystyle A$:

$\displaystyle A\times I = I\times A = A$

You then need to know that, if $\displaystyle A$ and $\displaystyle B$ are 2x2 matrices and $\displaystyle A\times B = I$, then $\displaystyle A$ and $\displaystyle B$ are*inverses*of each other. This is written $\displaystyle B= A^{-1}$ and $\displaystyle A = B^{-1}$.

So the matrix $\displaystyle \begin{pmatrix}a&b\\c&d \end{pmatrix}$ is the inverse of the matrix $\displaystyle \begin{pmatrix}3&2\\1&-1 \end{pmatrix}$. There's a formula for the inverse of a 2x2 matrix here: The inverse of a 2x2 matrix - mathcentre

If you use that formula, you'll find that:

$\displaystyle \begin{pmatrix}a&b\\c&d \end{pmatrix} = \frac{1}{5} \begin{pmatrix}1&2\\1&-3 \end{pmatrix}$

I hope that answers the question.

Grandad

- Feb 16th 2009, 11:02 AMstapel
If you're not familiar with the general process, try some online lessons regarding

**finding matrix inverses**.

If you are asking how to complete the exercise, try some online lessons regarding**matrix multiplication**. (**This lesson**has an animation that some students find helpful.)

Have fun! :D