multiplication of matrices

[RachelB]

I need help with multiplying matrices. I only have two problems that I can't figure out. The directions say "Find the product. If it is not defined, state the reason."

The problems are these:
1)

  [ -6  -2 ] [ -1   4 ]
  [  0   3 ] [ -5   3 ]

2)

  [  6.0   0   ] [ 1     0   ]
  [ -0.2   0.2 ] [ 1.5  -0.5 ]
  [  2.9   0.3 ]

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Edited by stapel -- Reason for edit: formatting

 

[galactus]

Your post is all mixed up.

Is the first one?:

\(\displaystyle \L\\\begin{bmatrix}-6&-2\\0&3\\\end{bmatrix}\cdot\begin{bmatrix}-1&4\\-5&3\end{bmatrix}=\begin{bmatrix}16&-30\\-15&9\end{bmatrix}\)


#2:

\(\displaystyle \L\\\begin{bmatrix}6&0\\-0.2&0.2\\2.9&0.3\end{bmatrix}\cdot\begin{bmatrix}1&0\\1.5&-0.5\end{bmatrix}=\begin{bmatrix}6&0\\0.1&-0.1\\3.35&-0.15\end{bmatrix}\)

 

[RachelB]

Thank you!!!!

 

[soroban]

Hello, Rachel!

I should have seen this post first . . .
So you do know how to multiply matrices
. . and you know about "row times column".

Then exactly where is your difficulty?

\(\displaystyle (1)\;\begin{bmatrix}-6 & -2 \\ \\ 0 & 3\end{bmatrix}\;\begin{bmatrix}-1 & 4 \\ \\ -5 & 3\end{bmatrix}\)

We have: \(\displaystyle \:\begin{bmatrix}-6 & -2 \\ \\ 0 & 3\end{bmatrix}\;\begin{bmatrix}-1 & 4 \\ \\ -5 & 3\end{bmatrix}\)

. . . . . .\(\displaystyle = \;\begin{bmatrix}(-6)(-1)\,+\,(-2)(-5)\; & \;(-6)(4)\,+\,(-2)(3) \\ \\ \\ (0)(-1)\,+\,(3)(-5) & (0)(4)\,+\,(3)(3)\end{bmatrix}\)

. . . . . .\(\displaystyle = \;\begin{bmatrix}16 & -30 \\ \\ \\ -15 & 9\end{bmatrix}\)