plsee can any one solve this determinants

Question

plsee  can any one solve this determinants

anonymous · Answer

https://www.khanacademy.org/math/algebra/algebra-matrices/inverting_matrices/v/finding-the-determinant-of-a-3x3-matrix-method-1

anonymous · Answer

can u given me hint to solve this
i know how to solve these determinants...but at this time
i not getting how to start up with these determiannats

hero · Answer

It's easy

anonymous · Answer

so should i explain how to start solving??

anonymous · Answer

yes, plsee

mertsj · Answer

mostly keeping track of stuff.

anonymous · Answer

|dw:1368183789438:dw|
do you see what i have done??

mertsj · Answer

The directions say "without expanding"

hero · Answer

What exactly is meant by "without expanding"?

anonymous · Answer

i was about ti ask that...^^

anonymous · Answer

**to

hero · Answer

And @mertsj disappears afterwards...

anonymous · Answer

without expanding means you have apply some steps like 
R1=3R1-R2

hero · Answer

It says "without expanding", so I'm guessing "reduction methods" are allowed.

anonymous · Answer

yes...i mean same @Hero have said

mertsj · Answer

I'm thinking co-factors???

hero · Answer

My reduction methods are different from yours @msingh

anonymous · Answer

okay

hero · Answer

Like for example I would keep reducing the matrix from 4 x 4 to 1 x 1, then divide by the interior of the matrix as needed.

anonymous · Answer

can any one plsee solve this
plseee

loser66 · Answer

I think you can eliminate by : 
keep R1 there                  1  3  9  27
3R1 - R2 --->R2 :        0  0  0  80
9 R1 - R3 ---> R3         0 0 80 240
3R3 -R4 ---> R4           0  80 0   0

 switch R2 to R4 the sign changes to negative, but you have an upper triangle determinant
   1  3  9   27
   0 80 0     0
   0   0  80  240
   0   0    0    80
don't forget the sign is negative . determinant of this just product of diagonal line

anonymous · Answer

what about second sum

loser66 · Answer

to me, my goal is making the upper or lower triangle, to the matrix whose the rows are not in perfect multiple of each other, just divided by the first entry to get first leading 1 and then multiple that row, and subtract to other, . done. you can do it, just trick

loser66 · Answer

sorry friend, my English is too bad
I mean divided R1 by 67 to get first leading 1

loser66 · Answer

sorry, 39 row 1 -row2 to get 0 at a_21. you know what I mean?

anonymous · Answer

okay

loser66 · Answer

good

anonymous · Answer

@Loser66 
plse explain me second sum

hero · Answer

What about my method?

anonymous · Answer

actually i little bit confuse i solving both the solutions

hero · Answer

Reduction Method might actually surprise your teacher.