1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If...
1. Let a,b,c,d be row vectors and form the matrix A whose rows
are a,b,c,d. If by a sequence of row operations applied to A we
reach a matrix whose last row is 0 (all entries are 0) then:
a. a,b,c,d are linearly dependent
b. one of a,b,c,d must be 0.
c. {a,b,c,d} is linearly independent.
d. {a,b,c,d} is a basis.
2. Suppose a, b, c, d are vectors in R4 . Then they form a...
1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is
(0,1) and second...
1. Let A be the 2x2 matrix in M_{2x2}(C), whose first row is
(0,1) and second row is (-1,0).
(a) Show that A is normal.
(b) Find (complex) eigenvalues of A.
(c) Find an orthogonal basis for C^2, which consists of
eigenvectors of A.
(d) Find an orthonormal basis for C^2, which consists of
eigenvectors of A.
Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))...
Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))
14. (3 points) Let B1 be the basis for M you found by row
reducing M and let B2 be the basis for M you found by row reducing
M Transpose . Find the change of coordinate matrix from B2 to
B1.