Matrix problems

**Mathgirl7** · December 2nd 2010, 04:02 PM

1) Find the matrix product, if possible, please.
[ 6 0 -4 ] [1]
[ 1 2 5 ] [2]
[ 10 -1 3] [3]

2) Decide whether the given matrices are inverse of each other. ( Check to see if their product is the identity matrix 1:

[ 1 0 0 ] [1 0 0]
[ -1 -2 3 ] and [ 0 0 1]
[ 0 1 0] [1/3 1/3 2/3]

Thank you!

**Soroban** · December 2nd 2010, 04:21 PM

Hello, Mathgirl7!

Exactly where is your difficulty?
If you don't know matrix multiplcation,
. . very few of us are willing to teach it here.

$\text{1) Find the matrix product, if possible.}$

. . $\begin{pmatrix} 6 & 0 &\text{-}4 \\ 1 & 2 & 5 \\ 10 & \text{-}1 & 3 \end{pmatrix} \begin{pmatrix}1 \\ 2 \\ 3 \end{pmatrix}$

$\text{Answer: }\;\begin{pmatrix}\text{-}6 \\ 15 \\ 17 \end{pmatrix}$

$\text{ 2) Decide whether the given matrices are inverses of each other.}$
. . . $\text{(Check to see if their product is the identity matrix }I.)$

. . $\begin{pmatrix}1 & 0 & 0 \\ \text{-}1 & \text{-}2 & 3 \\ 0 & 1 & 0 \end{pmatrix} \begin{pmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ \frac{1}{3} & \frac{1}{3} & \frac{2}{3} \end{pmatrix}$

Yes, they are inverses of each other.

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