I found the dual basis for each of the following bases for R^3: (a) {(1,0,0),(0,1,0),(0,0,1)}, (b) {(1,-2,3),(1,-1,1),(2,-4,7)}. -Mark R. Rowe

I provided a Kronecker delta d(ij) (written) dual-basis list is a 3x3 (array) list of phi(i) linear-mappings, gave three distinct systems of linear equation's have three corresponding vector solutions with components are coefficient numbers associated with the (found) basis (obviously is a vector-set with three vectors, where each vector has 3 components, a list of 3 numbers the same) is a dual-basis for the given bases, (for R^3) shown in the problem written here.

-Mark R. Rowe

The (two) photos shown above, are photos of a supplementary textbook (that aligns with linear algebra, advanced linear advanced physics, advanced engineering, and quantitative analysis) I have been working in since December 2017.

Buy this book on BarnesAndNoble.com, click on the (url) link below.

https://www.barnesandnoble.com/w/schaums-outline-of-linear-algebra-sixth-edition-seymour-lipschutz/1126078887?ean=9781260011449

-Mark R. Rowe