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FrogPad
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Please excuse the lack of latex, I'm in somewhat of a hurry and I do not have the time to lookup the latex syntax for matrices. With that out of the way, here is my question?
For an upcoming test question we were given example questions that may or may not appear on the test.
One question was given as:
Does matrix A belong to span(A_1,A_2,A_3)
A_1 = (1 2)
(3 4)
A_2 = ...
A_3 = ...
or for which values of [tex] \alpha [/tex]
--------
NOTE:
The syntax of A_1 is just what I'm using it to make it readable, thus:
a_11 = 1
a_12 = 2
a_21 = 3
a_22 = 4
--------
So, as you can see the question is not really detailed. It's just to give us an idea of the question. If the question was something like:
does [tex] \vec{V} [/tex] belong to span(A_1,A_2) where A_1=(1,4,3)^T , A_2=(-2,-1,0)^T
Then I definitely understand how to solve the problem. I'm just confused with the comment of, does this matrix belong, and where A_1 will equal something like:
(a b)
(c d)
Would it make sense to solve the problem like this:
* If we use the given problem above.
----
Does matrix A belong to span(A_1,A_2,A_3)
A_1 = (1 2)
(3 4)
A_2 = ...
A_3 = ...
----
* Then write A_n as a vector like:
Does the matrix A (where A=something like (a1,a2,a3,a4)^T ) belong to span(A_1,A_2,A_3)
where A_n = something like (a,b,c,d)^T
Ok, sorry if this is confusing... I just feel like I don't understand well enough what the question is asking. Also, one last thing... when someone says span(A_1,A_2)
where A_1 = (a b)
(c d)
does that mean that A_1 is in the vector space R^4 and is that the same as R^(2x2)?
thank you. and again I apologize for not using tex. (i'm just in a hurry here)
:)
thanks guys
For an upcoming test question we were given example questions that may or may not appear on the test.
One question was given as:
Does matrix A belong to span(A_1,A_2,A_3)
A_1 = (1 2)
(3 4)
A_2 = ...
A_3 = ...
or for which values of [tex] \alpha [/tex]
--------
NOTE:
The syntax of A_1 is just what I'm using it to make it readable, thus:
a_11 = 1
a_12 = 2
a_21 = 3
a_22 = 4
--------
So, as you can see the question is not really detailed. It's just to give us an idea of the question. If the question was something like:
does [tex] \vec{V} [/tex] belong to span(A_1,A_2) where A_1=(1,4,3)^T , A_2=(-2,-1,0)^T
Then I definitely understand how to solve the problem. I'm just confused with the comment of, does this matrix belong, and where A_1 will equal something like:
(a b)
(c d)
Would it make sense to solve the problem like this:
* If we use the given problem above.
----
Does matrix A belong to span(A_1,A_2,A_3)
A_1 = (1 2)
(3 4)
A_2 = ...
A_3 = ...
----
* Then write A_n as a vector like:
Does the matrix A (where A=something like (a1,a2,a3,a4)^T ) belong to span(A_1,A_2,A_3)
where A_n = something like (a,b,c,d)^T
Ok, sorry if this is confusing... I just feel like I don't understand well enough what the question is asking. Also, one last thing... when someone says span(A_1,A_2)
where A_1 = (a b)
(c d)
does that mean that A_1 is in the vector space R^4 and is that the same as R^(2x2)?
thank you. and again I apologize for not using tex. (i'm just in a hurry here)
:)
thanks guys