Question

Consider the following system of linear equations:

x+3y+4z=b1

2x+2y+z=b2

3x - 3y - 9z = b3

(a) Calculate the determinant of the coeffcients matrix of the above system.
(b)(i) What can you conclude (from (a)) about the solution set of this system?
(ii) What conditions must b1, b2, and b3 satisfy for the above system to have solutions?

Answer 1

Explanation:

Given is a system of equations as

`x+3y+4z=b1\\2x+2y+z=b2\\3x - 3y - 9z = b3`

Ax=B

a)where A=
`\left[\begin{array}{ccc}1&3&4\\2&2&1\\3&-3&-9\end{array}\right]`

=0

b)So system has no unique solution

c)If B =0 then this has an infinite solutions

i..e. b1=b2=b3 =0 to haveinfinite solutions