Question

find the value of the 3x3 matrix
[-6,-3,-5]
[ 5, 7, -6]
[3, 9, 9]

Answer 1

find the inverse of the matrix if it exists
[3, -1]
[-10 ,9]

Answer 2

solve the system by using a matrix equation
2x-3y=3
5x-7y=9

Answer 3

@amistre64 @help123please. @Ashleyisakitty

Answer 4

@terenzreignz

Answer 5

can you help with these?

Answer 6

Value of a 3x3 matrix?

Answer 7

yea the first one

Answer 8

You mean determinant?

Answer 9

um im not sure yea probably

Answer 10

my choices are
-635
-631
-633 and
-636

Answer 11

i did the work and i think its -635 but needed a second opinion

Answer 12

It isn't. Could you show me how you did it?

Answer 13

i multiplied the numbers diagnoly

Answer 14

then added

Answer 15

Yeah.. so show me. Need to see where you made the error

Answer 16

ok [-6,-3,-5]
[ 5, 7, -6]
[3, 9, 9]
so it would be -6* 9*-6 +-5*7*3+ 5*-3*9 right?

Answer 17

That results in 84...

Answer 18

yea im noy sure.. is that how you do it though?

Answer 19

No... think of it this way... You have a matrix...
\[\Large \left[\begin{matrix}a & b & c\\d&e&f\\g&h&i\end{matrix} \right]\]

Answer 20

okay

Answer 21

To get its determinant... copy the first and second columns and attach them to the right...
\[\Large \left[\begin{matrix}a & b & c\\d&e&f\\g&h&i\end{matrix} \right|\left.\begin{matrix}a&b\\d&e\\g&h\end{matrix}\right]\]

Answer 22

Catch me so far?

Answer 23

yes i think so

Answer 24

Okay, now you multiply diagonally, and add the products...
\[\Large \left[\begin{matrix}\color{red}a & \color{green}b & \color{blue}c\\d&\color{red}e&\color{green}f\\g&h&\color{red}i\end{matrix} \right|\left.\begin{matrix} a&b\\\color{blue}d&e\\\color{green}g&\color{blue}h\end{matrix}\right]\]

Answer 25

oh okay

Answer 26

So you get...
\[\Large \color{red}{aei}+ \color{green}{bfg}+\color{blue}{cdh}\] (this is not the entire determinant yet)

Answer 27

i got -549

Answer 28

And then, multiply THESE diagonals (this time, starting from the bottom)
\[\Large \left[\begin{matrix}a & b & \color{red}c\\d&\color{red}e&\color{green}f\\\color{red}g&\color{green}h&\color{blue}i\end{matrix} \right|\left.\begin{matrix}\color{green}a&\color{blue}b\\\color{blue}d&e\\g&h\end{matrix}\right]\]
but you NEGATE them...
\[\Large -\color{red}{gec}-\color{green}{hfa}-\color{blue}{idb}\]

Answer 29

okay one min

Answer 30

84?

Answer 31

don't forget the negative signs...

Answer 32

so -84

Answer 33

So that the total determinant is
\[\Large \color{red}{aei}+ \color{green}{bfg}+\color{blue}{cdh} -\color{red}{gec}-\color{green}{hfa}-\color{blue}{idb}\]

Answer 34

So, what's your answer?

Answer 35

would it be -633 then?

Answer 36

That is correct :)

Answer 37

thank you! can you help with the next two then ill not bother you?

Answer 38

Can't. I have to go now :)
Sorry... I'm sure there's someone here who'd be more than willing to help :)

Answer 39

okay thank you soo much!