16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 8.1.5

Inner Product Spaces

Mathematics — Linear Algebra · inner-products

Problem

Let ( ∣ )( \ | \ ) be the standard inner product on R2R^2. (a) Let α=(1,2)\alpha = (1, 2), β=(−1,1)\beta = (-1, 1). If γ\gamma is a vector such that (α∣γ)=−1(\alpha|\gamma) = -1 and (β∣γ)=3(\beta|\gamma) = 3, find γ\gamma. (b) Show that for any α\alpha in R2R^2 we have α=(α∣ϵ1)ϵ1+(α∣ϵ2)ϵ2\alpha = (\alpha|\epsilon_1)\epsilon_1 + (\alpha|\epsilon_2)\epsilon_2.

Related theory

Browse the problem library