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

herbariak1 2022-05-19 Answered
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 )
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

fongama33
Answered 2022-05-20 Author has 13 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.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-05-07
Solve for the variables w and x in the system of equations:
{ 5 w + 4 x = 2 5 w + 2 x = 3
asked 2022-07-10
find the solution to the problem y = ( 1 1 0 1 ) y , y ( 0 ) = ( 4 0 )
I know i have to find the eigenvalues and eigenvectors of the matrix A = ( 1 1 0 1 )
there's only one eigenvalue which is 1 and only "one" eigenvector and we can choose ( 1 0 )
but now I dont know what to do.
what comes next?
asked 2022-07-03
How find this linear equation
let a R,then solve this follow equation:
{ x 1 x 2 x 3 x n = 2 a x 1 + 3 x 2 x 3 x n = 4 a x 1 x 2 + 7 x 3 x n = 8 a x 1 x 2 x 3 + ( 2 n 1 ) x n = 2 n a
asked 2022-05-05
Solve for the variables x and y in the system of equations:
{ 4 x + 4 y = 3 2 x + 6 y = 2
asked 2022-08-02
For what value(s) of h is the linear system consistent?
6x1 ? 8x2 = h
?9x1 + 12x2 =?1
asked 2022-09-22
y=(20x+3)r+x and y is 50. What is x and r values?
asked 2022-05-21
Solving a set of recurrence relations
A n = B n 1 + C n 1
B n = A n + C n 1
C n = B n + C n 1
D n = E n 1 + G n 1
E n = D n + F n 1
F n = G n + C n
G n = E n + F n 1
which I would like to solve, with the goal of eventually finding an explicit form of E n . I started out by looking at only A n , B n and C n , and found a formula for A n .
A n = 1 / 3 3 ( 2 + 3 ) n 1 / 3 3 ( 2 3 ) n
but I cant seem to find the right trick this time.