Solution Found!
The solutions (x, y, z) of a single linear equation ax +
Chapter , Problem 3E(choose chapter or problem)
The solutions (x, y, z) of a single linear equation ax + by + cz = d form a plane in ?3& when a, b, and c are not all zero. Construct sets of three linear equations whose graphs (a) intersect in a single line, (b) intersect in a single point, and (c) have no points in common. Typical graphs are illustrated in the figure.
Questions & Answers
QUESTION:
The solutions (x, y, z) of a single linear equation ax + by + cz = d form a plane in ?3& when a, b, and c are not all zero. Construct sets of three linear equations whose graphs (a) intersect in a single line, (b) intersect in a single point, and (c) have no points in common. Typical graphs are illustrated in the figure.
ANSWER:Solution to 3E:Step 1: We given the linear equation ax +by +cz = d form a plane in R3 when a , b, c not all zero.In a system of three linear equation each equation represent a plane in three dimensional space. If the three planes meet at a single line then the each point on the line will be the solution to the given system of equations and the solution set is infinite .The system is consistent and has infinite number of solutions.The system of equation in three variables can be expressed as follows. AX = BWhere A is a 33 matrix and B is a 31 matrix.