Linear Algebra - Taleem-E
... An indexed set { v1, … , vp } of two or more vectors, with v1 0 , is linearly dependent if and only if some vj (with j 1) is a linear combination of the preceding vectors, v1, … , vj-1. ...
... An indexed set { v1, … , vp } of two or more vectors, with v1 0 , is linearly dependent if and only if some vj (with j 1) is a linear combination of the preceding vectors, v1, … , vj-1. ...
Solution
... (7) If V is isomorphic to W , then V ∗ is isomorphic to W ∗ . Solution: True. I believe this was proven in lecture. Remark: Here is a line of reasoning that works in the finite-dimensional setting: “By the construction of the dual basis, if V is finite-dimensional, then dim(V ) = dim(V ∗ ), so V is ...
... (7) If V is isomorphic to W , then V ∗ is isomorphic to W ∗ . Solution: True. I believe this was proven in lecture. Remark: Here is a line of reasoning that works in the finite-dimensional setting: “By the construction of the dual basis, if V is finite-dimensional, then dim(V ) = dim(V ∗ ), so V is ...
