

Let A be an m x 7 matrix of rank r such that Null(A) is a plane, and Ax = b is always consistent. Then the rank r of A is The nullity of A The dimension of Col(A)) is m = Let T(v) = Av. Is T one-to-one? Is T onto? T: RP → R9, where p = and q = 5 2 5 5 No Yes 7 5 No Yes 3 2 0 1 Cannot be determined. Cannot...
3. (15 pts) Let A be an m x n matrix with rank r, and let V = C(A). (a) V CIRP for what p? (b) What is V. in terms of a fundamental subspace for A? (c) How many vectors are in a basis for V, and how many in a basis for v 1? (d) For what m, n, and r docs Ax=b have a solution for every b? (e) Is a set of r vectors in V...
7. Let A be a 4 x 3 matrix, and let b and y be two arbitrary vectors in R. We are told that the system Ax- b has a unique solution. What can you say about the number of solutions of the system Ax - y? Explain your answer. 8. Let u. v, w, b be arbitrary vectors in R". Suppose that b = x1u+xy+23w for some scalars i, r23. Show that Span u, v, w, b Span u,...
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.)...
The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax 0?
How can I get the (a) 3*2 matrix A?
x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
(a) Why is it impossible for a 3 x 4 matrix A to have rank 4 and dim Nul A = 0? (b) What is the rank of a 6 x 8 matrix whose null space is three-dimensional? (c) If possible, construct a 3 x 5 matrix B such that dim Nul B =3 and rank B = 2. Explain your reasoning. (d) Construct a 4 x 3 matrix C with rank 1. It need not be complicated.
Let A be an m × n matrix The image of A is the set of vectors m(A) = {y : y = Ax for some x E Rn). which is a vector space The dimension of im(A) is called the rank of A, denoted by rank(A) (a) Find the rank of the matrix -62 1110 142 441 100-234 -1786478 46 -115 -46 -46 69 -122 85 150 174 -685 and enter in the box below rank(A) in应答 评分: 01...
83.016. My Notes Ask Your Ta Let A be a nonzero 3 x 5 matrix. (a) What is the maximum rank that A can have? (b) If rank(A B) 2, then for what value(s) of rank(A) is the system AX - B, B as a comma-separated list.) o, inconsistent? (Enter your answers For what value(s) of rank(A) is the system consistent? (Enter your answers as a comma-separated list.) (e) If rank(A) 2, then how many parameters does the solution of...
1. Let A be an m x n matrix. Determine whether each of the following are TRUE always or FALSE sometimes. If TRUE explain why. If FALSE give an example where it fails. (a) If m n there is at most one solution to Ax = b. always solve Ax b (b) If n > m you can (c) If n > m the null space of A has dimension greater than zero. (d) If n< m then for some...