matrix q23e5 w: evaluate determinant *

[tamiatha]

evaluate

12 5 -2
-3 0 1
-5 4 2

my solution
i used the diagonals/cross multiplying method

12 5 -2 5 -2
-3 0 1 0 1
-5 4 2 4 2

24+20+(-4)-10-25-(-4)
5-(-4)
answer=9

i tired to use expansion by minors method and got -67 but was not confident in how i arrived at that answer
help please

 

[Mrspi]

Re: matrix q23e5

evaluate

12 5 -2
-3 0 1
-5 4 2

my solution
i used the diagonals/cross multiplying method

12 5 -2 5 -2
-3 0 1 0 1
-5 4 2 4 2

24+20+(-4)-10-25-(-4)
5-(-4)
answer=9

i tired to use expansion by minors method and got -67 but was not confident in how i arrived at that answer
help please

When you re-copy columns 1 and 2, your array should look like this:

12    5    -2   12    5
-3    0     1   -3    0
-5    4     2   -5    4

Now, when you do the multiplications on the diagonals going down, your VERY FIRST multiplication is 12*0*2....how does that become 24?

And the first diagonal multiplication going up is (-5)*0*(-2). How does THAT become 10??

It is YOUR responsibility to make sure you've done the ARITHMETIC correctly. It looks to me like you are not being very careful with your work, and are expecting US to find and correct all of your careless errors.

 

[tamiatha]

Re: matrix q23e5 w

:x
you are soooo right
careless mistakes are a waste of everyone's time
i am now going off line-going to get my textbook out and go back over the matrix chapter-not only did i make mathematical errors but i chose different lines to multiply by than you did
i WILL return with another ,hopefully proper, solution
thank u

 

[tamiatha]

Re: matrix q23e5 w

ok
i got it
the value of the determinant is 77

am i right
i will show you my work if it is not
no careless mistakes this time..i hope

 

[Mrspi]

Re: matrix q23e5 w

ok
i got it
the value of the determinant is 77

am i right
i will show you my work if it is not
no careless mistakes this time..i hope

Please DO show us your work, because 77 is not even close to the value of the determinant for the given matrix.

 

[tamiatha]

Re: matrix q23e5 w

12 5 -2 12 5
-3 0 1 -3 0
-5 4 -2 5 4

12 x 0 x 2 = 0
5 x 1 x -5 = -25
-2 x -3 x 4 =24

5 x 0 x -2 = 0
4 x 1 x 12 = 48
2 x -3 x 5 = 30

0 + (-25) + 24 - 0 - 48 - (-30) = 77

 

[Deleted member 4993]

Re: matrix q23e5 w

12 5 -2 12 5
-3 0 1 -3 0
-5 4 -2 5 4

12 x 0 x 2 = 0
5 x 1 x -5 = -25
-2 x -3 x 4 =24

5 x 0 x -2 = 0
4 x 1 x 12 = 48
- 2 x -3 x 5 = 30

0 + (-25) + 24 - 0 - 48 - (+30) = -25 + 24 -48 - 30 = 24 - 103 = -79..................77

 

[Mrspi]

Re: matrix q23e5 w

Working with the "expanded matrix," the one produced by recopying columns 1 and 2, I see this:

Code: 

    12    5    -2   12    5
    -3    0     1   -3    0
    -5    4     2   -5    4

Select all

Multiplying DOWN on the diagonals, you have this:

12*0*2 + 5*1*(-5) + (-2)*(-3)*4, which gives you 0 + (-25) + 24, or -1

Multiplying UP on the diagonals, you have
-5*0*(-2) + 4*1*12 + 2*(-3)*5, or 0 + 48 + (-30), which is 18

Now...

You take the sum of the "downward diagonals" MINUS the sum of the "upward diagonals":

-1 - (18)

That does NOT give you anything close to 77.

AND, just to check this, I used my graphing calculator to calculate the determinant of the given matrix, and I got the same thing I did by doing the arithmetic by hand.

If I've missed something here, I sure would appreciate one of the volunteers showing my error.

 

[Deleted member 4993]

Re: matrix q23e5 w

Well, you see - she changed the problem - now a(3,3) = -2 (as opposed to +2)

 

[Mrspi]

Re: matrix q23e5 w

Well, you see - she changed the problem - now a(3,3) = -2 (as opposed to +2)

Ah thanks, Subhotosh Khan. Silly me...I assumed the problem had not changed from when it was originally posted. It's hard to get the right answer when you're working with incorrect data.