Partially answer 12.1

_code/pset_07/cpp/svd.cpp

@@ -47,8 +47,8 @@ int main() {
 
     Eigen::MatrixXd mat(n_samples, 2);
     for (uint32_t i = 0; i < n_samples; ++i) {
-        mat(i, 0) = samples[i];
-        mat(i, 1) = 1;
+        mat(i, 0) = 1;
+        mat(i, 1) = samples[i];
     }
 
     // Need at least ThinU and ThinV to use mat_svd.solve.

_psets/07.md

@@ -2,6 +2,19 @@
 title: Problem Set 7 (Function Fitting)
 ---
 
+## 1
+
+Generate 100 points $$x$$ uniformly distributed between 0 and 1, and let $$y = 2 + 3x + \zeta$$,
+where $$\zeta$$ is a Gaussian random variable with a standard deviation of 0.5. Use an SVD to fit
+$$y = a + bx$$ to this data set, finding $$a$$ and $$b$$. Evaluate the errors in $$a$$ and $$b$$
+using equation (12.34), by bootstrapping to generate 100 datasets, and from fitting an ensemble of
+100 independent data sets.
+
+I used [Eigen](http://eigen.tuxfamily.org/index.php?title=Main_Page) to compute the SVD (in C++).
+My code is
+[here](https://gitlab.cba.mit.edu/erik/nmm_2020_site/-/tree/master/_code/pset_07/cpp/svd.cpp). I
+found $$a = 2.10697$$ and $$b = 2.91616$$.
+
 ## 3
 
 {:.question}