Solve the following systems of linear equations. x1 + x2 − 2x3 + 3x4 + 2x5 = 6 3x1 + 3x2 − x3 + x4 + x5 = 12 2x1 + 2x2 − x3 + x4 − 2x5 = 5 4x1 + 4x2 + x3 − 3x5 = 16 8x1 + 5x2 − 2x3 − x4 + 2x5 = 29

x1 =  5

x2 = -1

x3 =  3

x4 =  2

x5 =  1

Step-by-step explanation:

x1   + x2   − 2x3 + 3x4 + 2x5 = 6

3x1 + 3x2 − x3   + x4   + x5   = 12

2x1 + 2x2 − x3   + x4   − 2x5 = 5

4x1 + 4x2 + x3    +0x4 − 3x5 = 16

8x1 + 5x2 − 2x3 − x4   + 2x5 = 29;

we apply the gauss jordan method

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: