Consider the following system of equations: 2x1 − 4x2 + 3x3 − x4 + 2x5 = 03x1 − 6x2 + 5x3 − 2x4 + 4x5 = 05x1 − 10x2 + 7x3 − 3x4 + 18x5 = 0.find the general solution of the system.

The system has a corresponding augmented matrix

Let's get this into reduced row echelon form.

Add 3(row 1) to -2(row 2), and add 5(row 1) to -2(row 3):

Multiply through row 2 by -1:

Add -1(row 2) to row 3:

Multiply through row 3 by 1/2:

Add row 3 to row 2:

Add -3(row 2) and row 3 to row 1:

Multiply through row 1 by 1/2:

This tells us

The matrix has rank 3, so we can pick 2 free variables, say and . Then the general solution to the system is

where .

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: