GOAL Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of P 2 given in Exercises 1 through 5 are subspaces of P 2 (see Example 16)? Find a basis for those that are subspaces. 1. { p ( t ) : p ( 0 ) = 2 }
GOAL Find a basis of a linear space and thus determine its dimension. Examine whether a subset of a linear space is a subspace. Which of the subsets of P 2 given in Exercises 1 through 5 are subspaces of P 2 (see Example 16)? Find a basis for those that are subspaces. 1. { p ( t ) : p ( 0 ) = 2 }
(1 point) Consider the vector space P2 of polynomials of degree at most 2. Let H be the subspace spanned by
2x² + x + 2, −2x² + x +5, and x².
a. The dimension of the subspace H is
b. Is {2x² + x + 2, −2x² + x + 5, x²} a basis for P₂?
choose
c. A basis for the subspace H is {
Enter a polynomial or a comma separated list of polynomials.
Linear Algebra Radiography and Tomography
a. Choose any two objects that produce the same radiograph and subtract them. What is special about the resulting object?
b. Show that the set of all invisible objects is a subspace of the vector space of all objects.
c. Find a set of objects that spans the space of all invisible objects. Is your set linearly independent? If not, find a linearly independent set of objects that spans the space of invisible objects. The linearly independent set you have found is a basis for the space of invisible objects.
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