Question

Given A (a matrix, I will type it as a comment), observe that the second column is the sum of the first and third columns. Find a nontrivial solution of Ax=0 without performing row operations.


How would one go about answering this?

Answer 1

The matrix is:
2 5 -3
-4 -9 -5
-2 -7 -5
3 7 4



How are matrices typed in on OpenStudy?

Answer 2

\[\left[\begin{matrix}? & ?&? \\ ? & ?&?\\?&?&?\\?&?&?\end{matrix}\right]\]

Answer 3

You have to use the \\ to add additional rows and &? to add addtional collumns @taljaards

Answer 4

you should learn that one way to multiply a matrix times a vector
is the 1st component of the vector times the first column of the matrix
plus the 2nd component of the vector times the 2nd column of the matrix
and so on....

if you want A x =0
where x is [a b c] (this is a vector, and should be written vertically)
then you want a * c1 + b*c2 + c*c3 =0
where c1,c2,c3 are the columns of A

the second column is the sum of the first and third columns
that says c2= c1+c3 or
c1-c2+c3 = 0
match that up with
a * c1 + b*c2 + c*c3 =0
to get the a , b and c components of the vector x