# Another matrix equation with unknown coefficients

• Dec 5th 2011, 09:29 AM
SweatingBear
Another matrix equation with unknown coefficients
Got another one that is also baffling me

Attachment 23008

After some simplification, I get

-x+2x=0
-x+10=1

Nope, no solutions for x!

5-5y=0
5-xy=1

Neither this one!

The book says x=9 and y=1. Help me?
• Dec 5th 2011, 10:19 AM
Opalg
Re: Another matrix equation with unknown coefficients
Quote:

Originally Posted by SweatingBear
Got another one that is also baffling me

$\displaystyle \begin{bmatrix}1&5\\ 1&x \end{bmatrix}\begin{bmatrix}-x&5\\2&-y \end{bmatrix} = \begin{bmatrix}1&0\\0&1 \end{bmatrix}$

After some simplification, I get

-x+2x=0
-x+10=1

Nope, no solutions for x!

5-5y=0
5-xy=1

Neither this one!

The book says x=9 and y=1. Help me?

As in the previous thread, the question is wrong. Either the book is full of misprints, or you are copying the questions very carelessly.

The first matrix should be $\displaystyle \begin{bmatrix}1&5\\ 2&x \end{bmatrix}$, not $\displaystyle \begin{bmatrix}1&5\\ 1&x \end{bmatrix}.$
• Dec 5th 2011, 10:37 AM
SweatingBear
Re: Another matrix equation with unknown coefficients
Quote:

Originally Posted by Opalg
As in the previous thread, the question is wrong. Either the book is full of misprints, or you are copying the questions very carelessly.

The first matrix should be $\displaystyle \begin{bmatrix}1&5\\ 2&x \end{bmatrix}$, not $\displaystyle \begin{bmatrix}1&5\\ 1&x \end{bmatrix}.$

Misprints. Thx.
By the way — how do you know how they are supposed to be?
• Dec 5th 2011, 10:52 AM
Opalg
Re: Another matrix equation with unknown coefficients
Quote:

Originally Posted by SweatingBear
By the way — how do you know how they are supposed to be?

These are inverse matrices, that is, two matrices whose product is the identity matrix $\displaystyle \begin{bmatrix}1&0\\0&1 \end{bmatrix}.$ There is a formula for the inverse of a matrix, which makes it easy to see what the question should be asking.