I need help figuring out the first problem on the following practice test. Thanks for your help!
http://www.math.gatech.edu/~carlen/1502F06/PT3F06.pdf
2006-10-25 16:36:53 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
And when I mean linear, I mean that in terms of linear algebra, not whether it's a straight line or not.
2006-10-25 16:45:24 · update #1
f is not linear, because f([0, 0, 0])≠[0, 0]. Any linear transformation will have 0 in its kernel.
g is linear, and given by the matrix:
[2, 3, 0]
[3, 0, -2]
h is linear, and given by the matrix:
[1, 1, 1]
[1, 0, 0]
None of the transformations are invertible, since they go from R³ to R².
2006-10-25 16:45:00 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
A linear function is a function of the first degree.
No exponents above "1" involved.
All numbers are mulitplied by "1", Divided by "1" and raised to the first power. Because you can do all three without changing the value of the number.
If the power is higher than "1" it is a non Linear Function. A linear function is one where the exponent of the power is "1"
2006-10-25 16:58:40 · answer #2 · answered by Anonymous · 0⤊ 0⤋
A function is linear if the highest exponent of the variable is 1 and the graph is a straight line.
2006-10-25 16:42:53 · answer #3 · answered by Diwata 1 · 0⤊ 1⤋
I think if you take the derivative and it's constant then the function is linear. This may not be the best mathematical definition though.
2006-10-25 17:17:48 · answer #4 · answered by NordicGuru 3 · 0⤊ 0⤋
if the equation of thefunction is of firstdegee of the type ax+by+c=0 then the function is linear
2006-10-25 16:46:41 · answer #5 · answered by raj 7 · 0⤊ 0⤋
A transformation T(x) defined on a vector space V is linear if, for any vectors x and y in V, and any scalar c,
1) T(x+y) = T(x) + T(y)
2) T(cx) = cT(x)
2006-10-25 16:45:13 · answer #6 · answered by James L 5 · 0⤊ 0⤋