Solution
... F ⊕∞ . Taking the standard basis {ei }∞ i=1 , where ei has a 1 in the ith position and 0s elsewhere, we see that the data of f consists exactly of a scalar in F for each i ∈ I. These add and scale pointwise. Thus f corresponds exactly to a vector in F ×∞ . Since F ×∞ is never isomorphic to F ⊕∞ we s ...
... F ⊕∞ . Taking the standard basis {ei }∞ i=1 , where ei has a 1 in the ith position and 0s elsewhere, we see that the data of f consists exactly of a scalar in F for each i ∈ I. These add and scale pointwise. Thus f corresponds exactly to a vector in F ×∞ . Since F ×∞ is never isomorphic to F ⊕∞ we s ...
PDF
... Figure 5 Effect of step size in Euler’s method. Can one solve a definite integral using numerical methods such as Euler’s method of solving ordinary differential equations? Let us suppose you want to find the integral of a function f (x) b ...
... Figure 5 Effect of step size in Euler’s method. Can one solve a definite integral using numerical methods such as Euler’s method of solving ordinary differential equations? Let us suppose you want to find the integral of a function f (x) b ...
test 2
... (a) If A is a 3 × 3 matrix and {~v1 , ~v2 , ~v3 } is a linearly dependent set of vectors in R3 , then {A~v1 , A~v2 , A~v3 } is also a linearly dependent set. (b) If A is a 3 × 3 invertible matrix and {~v1 , ~v2 , ~v3 } is a linearly independent set of vectors in R3 , then {A~v1 , A~v2 , A~v3 } is al ...
... (a) If A is a 3 × 3 matrix and {~v1 , ~v2 , ~v3 } is a linearly dependent set of vectors in R3 , then {A~v1 , A~v2 , A~v3 } is also a linearly dependent set. (b) If A is a 3 × 3 invertible matrix and {~v1 , ~v2 , ~v3 } is a linearly independent set of vectors in R3 , then {A~v1 , A~v2 , A~v3 } is al ...
