We solve the problem by checking linear dependency and independency of the set. Please find below the complete solution.
1. Does the set of vectors 0)(0) have the same span as the set 001 Justify your answer.
Justify your answer: a) Could a set of three vectors in R5 span all of R5? You have to provide a short argument which shows why your answer is correct. b) Suppose A is a 3X3 matrix and b is a vector in R3 with the property that Ax =b has a unique solution. Explain why the columns of A must span all of R3.
Find an explicit description of Nul A by listing vectors that span the null space. 130 - 20 A=001 - 40 000 0 1 A spanning set for Nul A is (Use a comma to separate answers as needed.)
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
Please write clear in the explanation thanks 1 2 0 -1 3 2 1 -1 2 1 oand RREF(A)- 1 3 -1 2 Suppose that A3 21 a. s there a unique solution to Ax-22 Justify your reasoning completely ?Justify your reasoning completely. b. Are the column vectors of A a basis for R? Justify your reasoning. c. Define geometrically the span of A. 1 2 0 -1 3 2 1 -1 2 1 oand RREF(A)- 1 3 -1 2...
(7) Consider the set W of vectors of the form | 4a + 36 1 0 a+b+c c-2a where a,b,c E R are arbitrary real numbers. Either describe W as the span of a set of vectors and compute dim W, or show that W is not a linear subspace of R. (8) Find a basis for the span of the vectors 16115 1-1/ 121, ܘ ܟ ܢܝ
Let B be the standard basis of the space P2 of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. 1-3t+ 2t?, - 4 + 9t-22, -1 + 412, + 3t - 6t2 Does the set of polynomials span P2? O A. Yes, since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R3. By isomorphism between...
(4) Find the span of the vectors You answer should be either: 0}, a 3 1 2 line through the origin, a plane through the origin, or R3. Determine which one it is. If it's a line or a plane, find its equation
1) Decide whether or not the set S of vectors in R3 actually spans R3. If S does not span R find a specific vector int R3 not in the span ()0)0
, 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...
I am looking for how to explain #4 part b. I have gotten the matrix A and I believe the answer is W = span{ v1 u2 u3 } however I'm not really sure if that is correct or not. Please give a small explanation. Also im not sure if I need to represent the vectors in A as columns or rows, or if either one works. For the next two problems, W is the subspace of R4 given by...