Answer:
Step-by-step explanation:
Given the system of homogeneous equations
x1 + 2x2 - 3x3 = 0 ................. 1
4x1 + 7x2 - 9x3 = 0 ................... 2
-x1 - 3x2 + 6x3 = 0..................... 3
First we will reduce the equation to two equations and two unknowns;
add equation 1 and 3;
2x2-3x2 +(-3x3+6x3) = 0
-x2 + 3x3 = 0
x2 = 3x3 .......... 4
Multiply equation 3 by 4 and add to equation 2;
equation 3 * 4 will give;
-4x1 - 12x2 + 24x3 = 0..................... 5
add equation 5 to equation 2;
7x2-12x2-9x3+24x3 = 0
-5x2 - 15x3 = 0 .......... 6
5x2 = 15x3
x2 = 3x3
Let x2 = k
From equation 4;
k = 3x3
x3 = k/3
substitute x2 = k and x3 = k/3 into equation 1 to get x1 in terms of k
From 1, x1 + 2x2 - 3x3 = 0
x1+2k-3(k/3) = 0
x1 +2k-k = 0
x1 +k = 0
x1 = -k
Writing the answer in vector form will give (x1. x2. x3) = (-k, k, k/3)
k(-1, 1, 1/3)
Hence the answer to the system of equation in vector form is k(-1, 1, 1/3) where k is any constant.
