For how many values of &#x03B1;<!-- α --> does this system of equations have infinitely many s

herbariak1

herbariak1

Answered question

2022-05-19

For how many values of α does this system of equations have infinitely many solutions ?
( 2 1 4 4 3 12 1 2 8 ) ( x y z ) = ( α 5 7 )

Answer & Explanation

fongama33

fongama33

Beginner2022-05-20Added 12 answers

The point is that the system has a kernel; since the column space is not 3-dimensional there are nontrivial linear combinations of the columns that vanish, namely multiples of x = 0 , y = 4 , z = 1. So given one solution, you find another by adding any element of this kernel. Do be sure to check your claim about there being exactly one α , though: not every line intersects every plane, and a given line intersects some planes infinitely often.

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