Matrix Problem. Urgent.?

Question

Use Gaussian Elimination to reduce the following system to
upper triangular form:

- 2x_1 + 8x_2 + 7x_3 = 45
3x_1 + 5x_2 + 2x_3 = 15
8x_1 + 2x_2 - 3x_3 = - 16

Does this system have a unique solution, no solution or an infinite number of solutions.

Points for all those who anwser.

Answer 1

-2 8 7 | 45
3 5 2 | 15
8 2 -3 | -16

(-1/2)R1 -> R1
1 -4 -3.5 | -22.5
3 5 2 | 15
8 2 -3 | -16

(-3)R1 + R2 -> R2
(-8)R1 + R3 -> R3
1 -4 -3.5 | -22.5
0 17 12.5 | 82.5
0 34 25 | 164

(1/17)R2 ->R2
1 -4 -3.5 | -22.5
0 1 12.5/17 | 82.5/17
0 34 25 | 164

(-34)R2 + R3 -> R3
1 -4 -3.5 | -22.5
0 1 12.5/17 | 82.5/17
0 0 0 | -1

I think it has no solutions (because of that last line).

Answer 2

We want to get a matrix with 1s on the diagonal [where -2, 5 and -3 are now] and 0s below.

First, we deal with the first column.

-2 + 8 + 7 = 45
3 + 5 + 2 = 15
8 + 2 - 3 = -16

R1 -> R1 + R2 (add row 2 to row 1 to obtain 1 for the top entry in the first column)

1 + 13 + 9 = 60
3 + 5 + 2 = 15
8 + 2 - 3 = -16

Now we need 0s below the first entry in the first column.
R2 -> R2 - 3R1
R3 -> R3 - 8R1

1 + 13 + 9 = 60
0 -34 - 25 = -165
0 -102 -75 = -496

Move on to the second column. Want to have 1 where -34 is now and 0 where -102 is.

R3 -> R3 - 3R2

1 + 13 + 9 = 60
0 -34 - 25 = -165
0 + 0 + 0 = -1

OOOps,
0=-1
!
This indicates the system has NO solutions!
(Another way to say this is the system is INCONSISTENT.)

Answer 3

Apologies for the formatting, not much I can do about it.

[-2 8 7 | 45]
[ 3 5 2 | 15]
[ 8 2 -3 | -16]
~
[1 -4 -3/2 | 45/2 ]
[ 3 5 2 | 15]
[ 8 2 -3 | -16]
~
[1 -4 -3/2 | 45/2 ]
[0 17 13/2 | -105/2 ]
[0 34 9 | -196]
~
[1 -4 -3/2 | 45/2 ]
[0 1 13/34 | -105/34 ]
[0 34 9 | -196]
~
[1 -4 -3/2 | 45/2 ]
[0 1 13/34 | -105/34 ]
[0 0 -4 | -91]
~
[1 -4 -3/2 | 45/2 ]
[0 1 13/34 | -105/34 ]
[0 0 1 | 91/4]

Hence the system has a unique solution.

Answer 4

An get admission to won't be able to be both 0 and a million concurrently, so assuming you mean both 0 or a million, then if the matrix had a million cellular, it will be both 0, or a million., if 2, then 00, 01, 10, 11 .. so for n cells 2^n diverse matrices..

Answer 5

you say points for all those who answer, there goin to get points anyway for answering ur question just like me

can i get best answer