1. ## Find the determinates

Where
\begin{bmatrix}
a & b & c \\
d & e & f \\
g & h & i\\
\end{bmatrix} WHERE THIS MATRIX EQUALS 7

\begin{bmatrix}
a & b & c \\
d & e & f \\
3g & 3h & 3i\\
\end{bmatrix}

FIND THE DETERMINATES OF THIS MATRIX

2. ## Re: Find the determinates

$|A B | = |A||B|$

$\begin{pmatrix}a &b &c \\d &e &f \\3g &3h &3i \end{pmatrix} = \begin{pmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &3 \end{pmatrix} \begin{pmatrix}a &b &c \\d &e &f \\g &h &i \end{pmatrix}$

$\left |\begin{pmatrix}a &b &c \\d &e &f \\3g &3h &3i \end{pmatrix}\right | = \left | \begin{pmatrix}1 &0 &0 \\0 &1 &0 \\0 &0 &3 \end{pmatrix}\right | \left | \begin{pmatrix}a &b &c \\d &e &f \\g &h &i \end{pmatrix}\right | = 3 \cdot 7 = 21$

3. ## Re: Find the determinates

btw the word is determinant

4. ## Re: Find the determinates

And there is only one to be found so the word should not be plural.

And you should have written "where the determinant of this matrix is 7", not "where this matrix is 7".

5. ## Re: Find the determinates

Thanks for the help guys. For the next one, it says a+d b+e and c+f for the top row. I know that for the first row it would be 1+? 0 0, but im not sure what I need to add in order to get the row below’s variable

6. ## Re: Find the determinates

Originally Posted by Cammy
Thanks for the help guys. For the next one, it says a+d b+e and c+f for the top row. I know that for the first row it would be 1+? 0 0, but im not sure what I need to add in order to get the row below’s variable
$\begin{pmatrix}a+d &b+e &c+f \\d &e &f \\g &h &i \end{pmatrix} = \begin{pmatrix}1 &1 &0 \\0 &1 &0 \\0 &0 &1 \end{pmatrix} \begin{pmatrix}a &b &c \\d &e &f \\g &h &i \end{pmatrix}$