Another matrix equation with unknown coefficients

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December 5th 2011, 09:29 AM
SweatingBear

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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?
December 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

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

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 $\begin{bmatrix}1&5\\ 2&x \end{bmatrix}$ , not $\begin{bmatrix}1&5\\ 1&x \end{bmatrix}.$
December 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 $\begin{bmatrix}1&5\\ 2&x \end{bmatrix}$ , not $\begin{bmatrix}1&5\\ 1&x \end{bmatrix}.$

Misprints. Thx.
By the way — how do you know how they are supposed to be?
December 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 $\begin{bmatrix}1&0\\0&1 \end{bmatrix}.$ There is a formula for the inverse of a matrix, which makes it easy to see what the question should be asking.