Page 312 - 35Linear Algebra

312 Least squares and Singular Values

Congratulations, you have reached the end of the book!

Now test your skills on the sample final exam.

17.3 Review Problems

Webwork: Reading Problem 1 ,

1. Let L : U → V be a linear transformation. Suppose v ∈ L(U) and you
have found a vector u ps that obeys L(u ps ) = v.

Explain why you need to compute ker L to describe the solution set of
the linear system L(u) = v.

Hint

2. Suppose that M is an m × n matrix with trivial kernel. Show that for
m
any vectors u and v in R :
T
T
T
T
• u M Mv = v M Mu.
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