(adsbygoogle = window.adsbygoogle || []).push({}); Show taht [itex] {a + bx + cx^2, a_{1} + b_{1} x + c_{1} x^2, a_{2} + b_{2} x + c_{2} x^2} [/itex] is a basis of P2 iff {(a,b,c) , (a1,b1,c1) , (a2,b2,c2)} is a basis of R3

suppose [itex] {a + bx + cx^2, a_{1} + b_{1} x + c_{1} x^2, a_{2} + b_{2} x + c_{2} x^2} [/itex] is a basis of P2 then

a linear combination of those three vectors would require all teh scalar multipliers to be zeros

but im not sure where to go from there... do i have to somehow write he basis of P2 as a basis of R3??

DOes the same apply for the only if part?

Determien whether the transformation has an iverse and if so then find the action of its inverse

T; R4 - > R4

T(x,y,z,t) = (x+y,y+z,z+t,t+x)

Both the preimage and the image have the same dimension i have to show that either t is onto or one to one

how owuld i show it is onto? Or one to one?? Do i simply line up x1s and y1s and see if they are equal if the image of them is equal??

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: MORE linear algebra

**Physics Forums | Science Articles, Homework Help, Discussion**