Concept explainers
In all parts of this problem, let V be the set of all
a. Represent V as the kernel of a matrix M. Find the rank of M and the dimension of V. Show that
b. Find all vectors of the form
that are contained in V. (Be prepared to deal with irrational numbers.) Can you form a basis of V consisting of such vectors?
c. Consider the linear transformation
d. Find the matrix A of F with respect to the basis
e. Find the matrix B of F with respect to your basis from part (b).
f. Find the change of basis matrix
g. Write an equation relating the matrices A, B, and S, and check that this equation holds for the matrices you found in parts (d), (e), and (f).
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Linear Algebra with Applications (2-Download)
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