Question

Evaluate the determinant for the following matrix:[1,4,4;5,2,2;1,5,5]

Answer 1

@agent0smith and @jim_thompson5910 can yall help me?

Answer 2

Screenshot.

Answer 3

http://www.purplemath.com/modules/determs2.htm

Answer 4

@agent0smith

Answer 5

idk i'm too tired to work it out, especially with you not posting it in an easy to read way.

Answer 6

[1,4,4;5,2,2;1,5,5] would be written as
\[\Large \begin{bmatrix}1 & 4 & 4\\5 & 2 & 2\\1 & 5 & 5\end{bmatrix}\]

Answer 7

i just did it the way that angent0smith told me to do and i got 0

Answer 8

So we have this determinant (vertical bars signal "determinant")
\[\Large \left|\begin{array}{ccc}1 & 4 & 4\\5 & 2 & 2\\1 & 5 & 5\end{array}\right|\]

Answer 9

okay

Answer 10

Copy over the first two columns and write them on the right side of the determinant
\[\Large \left|\begin{array}{ccc|cc}{\color{red}{1}} & {\color{green}{4}} & 4 & {\color{red}{1}} & {\color{green}{4}} \\{\color{red}{5}} & {\color{green}{2}} & 2 & {\color{red}{5}} & {\color{green}{2}}\\{\color{red}{1}} & {\color{green}{5}} & 5 & {\color{red}{1}} & {\color{green}{5}}\end{array}\right.\]

Answer 11

okay

Answer 12

So we have this
\[\Large \left|\begin{array}{ccc|cc}1 & 4 & 4 & 1 & 4\\5 & 2 & 2 & 5 & 2\\1 & 5 & 5 & 1 & 5\end{array}\right.\]

Answer 13

Now what we do next is highlight the diagonals like shown in that link

Let's go one diagonal at a time
\[\Large \left|\begin{array}{ccc|cc}{\color{red}{1}} & 4 & 4 & 1 & 4\\5 & {\color{red}{2}} & 2 & 5 & 2\\1 & 5 & {\color{red}{5}} & 1 & 5\end{array}\right.\]

What happens when you multiply those red values together?

Answer 14

=10

Answer 15

correct, how about when you do this diagonal

\[\Large \left|\begin{array}{ccc|cc}1 & {\color{red}{4}} & 4 & 1 & 4\\5 & 2 & {\color{red}{2}} & 5 & 2\\1 & 5 & 5 & {\color{red}{1}} & 5\end{array}\right.\]

Answer 16

=8

Answer 17

4*5*5=100

Answer 18

\[\Large \left|\begin{array}{ccc|cc}1 & 4 & {\color{red}{4}} & 1 & 4\\5 & 2 & 2 & {\color{red}{5}} & 2\\1 & 5 & 5 & 1 & {\color{red}{5}}\end{array}\right.\]
yes 4*5*5 = 100

Answer 19

1*2*4=8
5*2*1=10
5*5*4=100

Answer 20

So far we have 10+8+100 = 118

Answer 21

10-8+8+100-10-100=0

Answer 22

correct. The final result will be 0

Answer 23

okay thanks

Answer 24

wolfram alpha confirms it

http://www.wolframalpha.com/input/?i=determinant(%5B%5B1,4,4%5D,%5B5,2,2%5D,%5B1,5,5%5D%5D)