Find all x in R that are mapped into the zero vector by the transformation x Ax for the given matrix A. 111 13 A 0 1-4 4 4 -16 28-36 Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is only one vector, which is x- + X 3
6. True or False: (a) An eigenvalue of the matrix A is a non-zero vector y such that Ac = Xū. (b) Let A be a 3 x 4 matrix. Then ker A is non-trivial. (e) Let A be an n x n matrix. Ta is injective (i.e. one-to-one) if and only if TA is surjective (i.e. onto). (d) If A is a singular matrix, then A must have an eigenvalue. (e) The set {A € M,(F): det(A) = +1}...
What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p of the vector b-5 onto this subspace? Pi P2 Ps What is the matrix P (P,) for the projection of R3 onto the subspace V spanned by the vectors 0 Pi3 12 P2 1 23 - P33 3 1 4 What is the projection p...
, A is a linear transformation that maps vectors x in 975 into vectors Let A= 0 -2 1 b in R2 Consider the set of all possible vectors b-Ax, where x is of unit length. What is the longest vector b in this set, and what unit length vector x is used to obtain it? You can use Matlab to save time with the computations, but please justify your answer. , A is a linear transformation that maps vectors...
Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of A d) For each column vector which is not a basis vector that you obtained in c), express it as a linear combination of the basis vectors for the range of...
22. (a) Find two vectors that span the null space of A 3 -1 2 -4 (b) Use the result of part (a) to find the matrix that projects vectors onto the null space of A. (c) Find two orthogonal vectors that span the null space of A. (d) Use the result of (c) to find the matrix that projects vectors onto the nul space of A. Compare this matrix with the one found in part (a). (e) Find the...
Problem 13. Let l be the line in R' spanned by the vector u = 3 and let P:R -R be the projection onto line l. We have seen that projection onto a line is a linear transformation (also see page 218 example 3.59). a). Find the standard matrix representation of P by finding the images of the standard basis vectors e, e, and e, under the transformation P. b). Find the standard matrix representation of P by the second...
b. Find the volume of the parallelepiped spanned by the vectors (t, 0,0), (1,2,-4), (0, t,-1). For what values of t will there be a zero volume? What can you say about the three vectors when the volume is zero? Using a 3D graphing program, include two graphs of the three vector, one where the volume is not zero and one where the volume is zero. (9pts) b. Find the volume of the parallelepiped spanned by the vectors (t, 0,0),...
4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto C(A) with its error vector. b) Find the least squares approximation, £, to the solution vector x of Ai- c) The least squares error is defined to be the length of the vector b - AX. Find this vector and its length. d) What is the relationship between A, , and p? 4 1|and b-l-2 Let A-13 a) Find the orthogonal projection p of b onto...
We were unable to transcribe this imageer the Toiowing imatrix and two vectors 13140 1 2 6 3 91 1 1 -3 0 -31 -2 (-2-61-53-3 er the Toiowing imatrix and two vectors 13140 1 2 6 3 91 1 1 -3 0 -31 -2 (-2-61-53-3