Do the three planes x 1 plus 4 x 2 plus 3 x 3 equals 5x1+4x2+3x3=5, x 2 minus 3 x 3 equals 1x2−3x3=1, and 3 x 1 plus 15 x 2 equals 123x1+15x2=12 have at least one common point of intersection? explain.

nswer:

No, they do not have any common point of intersection.



Step-by-step explanation:

Do the three planes have a common point of intersection?

X1 + 4X2 + 3X3 = 5

X2 - 3X3 = 1

3X1 + 15X2 = 15

Using matrix method

First, convert the given equation to matrix equivalent

Subtract Row1 from Row 3

Row3 = Row3 - Row1

Inconsistent planes.

Planes from row 2 and row 3 do not intersect and they do no have anything in common.

Hence, we do not need to move further

step-by-step explanation:

|ab| = 1.4 = 4

h = 1.4 = 4

a(abc) area = 4.4 = 16/2 = 8

area of abc = 8 cm^2

good luck ! ; )

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.