# What makes this matrix true?

• Apr 25th 2010, 03:14 PM
Anemori
What makes this matrix true?
what makes this matrix true?

$\displaystyle (\begin{array}{|ccc|}x&2&-1\\0&y&w\end{array} + \begin{array}{|ccc|}0&1&2\\0&0&2\end{array}) * \begin{array}{|ccc|}1&1\\3&z\\4&2\end{array} = \begin{array}{|ccc|}12&4\\2&2\end{array}$

• Apr 25th 2010, 03:27 PM
pickslides
Perform the operations as the problem suggests.

1. add the matrices inside the brackets.
2. multiply the result with the remaining LHS matrix.

Show your work to there, i will then help further.
• Apr 25th 2010, 07:00 PM
Anemori
Quote:

Originally Posted by pickslides
Perform the operations as the problem suggests.

1. add the matrices inside the brackets.
2. multiply the result with the remaining LHS matrix.

Show your work to there, i will then help further.

$\displaystyle \begin{array}{|ccc|}x+0&2+1&-1+2\\0+0&y+0&w+2\end{array} = \begin{array}{|ccc|}x&3&1\\0&y&w+2\end{array}$

x,3,1
0,y,w+2
*
1,1
3,z
4,2
=
x,9,1
0,2y,,2w,4

This is what i got....
• Apr 26th 2010, 03:00 AM
pickslides
Quote:

Originally Posted by Anemori

x,3,1
0,y,w+2
*
1,1
3,z
4,2
=
x,9,1
0,2y,,2w,4

I get

$\displaystyle \left(\begin{array}{ccc}x&3&1\\0&y&w+2\end{array}\ right) \times \left(\begin{array}{ccc}1&1\\3&z\\4&2\end{array}\r ight) = \left(\begin{array}{cc}x+9+4&x+3z+2\\3y+4(w+2)&yz+ 2(w+2)\end{array}\right)$

Now solve

$\displaystyle \left(\begin{array}{cc}x+9+4&x+3z+2\\3y+4(w+2)&yz+ 2(w+2)\end{array}\right) = \left(\begin{array}{cc}12&4\\2&2\end{array}\right)$

Might need to do some expanding on the LHS first!
• Apr 26th 2010, 06:10 AM
Anemori
Quote:

Originally Posted by pickslides
I get

$\displaystyle \left(\begin{array}{ccc}x&3&1\\0&y&w+2\end{array}\ right) \times \left(\begin{array}{ccc}1&1\\3&z\\4&2\end{array}\r ight) = \left(\begin{array}{cc}x+9+4&x+3z+2\\3y+4(w+2)&yz+ 2(w+2)\end{array}\right)$

Now solve

$\displaystyle \left(\begin{array}{cc}x+9+4&x+3z+2\\3y+4(w+2)&yz+ 2(w+2)\end{array}\right) = \left(\begin{array}{cc}12&4\\2&2\end{array}\right)$

Might need to do some expanding on the LHS first!

What do you mean expand? How do you do that?
• Apr 26th 2010, 01:58 PM
pickslides
Quote:

Originally Posted by Anemori
What do you mean expand? How do you do that?

I mean the bottom terms in the LHS matrix.

I.e. $\displaystyle 3y+4(w+2) = 3y+4w+8$

You then need to make 4 equations and solve them simultaneously.

Equate the term in each corresponding postition from each matrix.

Here's the first.

$\displaystyle x+9+4= 12$
• Apr 26th 2010, 04:44 PM
Anemori
Thanks (Clapping).. i got it...