Question

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.

Answer 1

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

$\left[\begin{array}{cccc}1&4&3&5\\0&1&3&1\\3&15&0&15\end{array}\right]$

Subtract Row1 from Row 3

Row3 = Row3 - Row1

$\left[\begin{array}{cccc}1&4&3&5\\0&1&3&1\\2&11&-3&10\end{array}\right]$

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