Math 410 Midterm 1 practice solutions
Problem 1: We row-reduce the
1
0
0
0
matrix to
0
1
1
1 2 1
,
0 3 3
0 3 3
and because two rows are equal, we know the matrix is singular and the
determinant is 0.
Problem 2: We start by writing
1 1
1 2
2 1
the aug
Math 410 Midterm 2 practice solutions
Problem 1: Given a matrix A, if it is complete (i.e. if it has a full set of
eigenvectors), one can put the eigenvalues of A in a diagonal matrix D and
the corresponding eigenvectors as columns in a matrix V and have
Math 410 Midterm 3 practice solutions
Problem 1: The vector in the vector space V = Spancfw_v 1 , v 2 , v 3 that is
closest to the vector z is the orthogonal projection of z onto V (lets call
it z ). We can simplify our calculations by noticing that v 3