Determine if the statement is true or false, and justify your answer. If u1, u2, u3...

Question

Question

math algebra

Answer 1

Answer #1

2ndependent- need not

Answer 2

Similar Homework Help Questions

Determine if the statement is true or false, and justify your answer. If u4 is not...

Determine if the statement is true or false, and justify your answer. If u4 is not a linear combination of {u1, u2, u3}, then {u1, u2, u3, u4} is linearly independent. A) False. Consider u1 = (1, 0, 0), u2 = (0, 1, 0), u3 = (0, 0, 1), u4 = (0, 1, 0). B) False. Consider u1 = (1, 0, 0), u2 = (1, 0, 0), u3 = (1, 0, 0), u4 = (0, 1, 0). C) True. The...
(1 point) Let u4 be a linear combination of {u1, U2, u3}. Select the best statement....

(1 point) Let u4 be a linear combination of {u1, U2, u3}. Select the best statement. OA. {u1, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. OB. {ui, U2, U3, U4} is always a linearly dependent set of vectors. OC. {ui, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, U2, U3, U4} is a linearly...
(1 point) Assume ug is not a linear combination of {u1, 42, u3}. Select the best...

(1 point) Assume ug is not a linear combination of {u1, 42, u3}. Select the best statement. A. {u1, U2, U3, U4} is never a linearly independent set of vectors. B. {U1, U2, U3, U4} is always a linearly independent set of vectors. C. {ui, U2, U3, U4} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. OD. {u1, 42, uz, u4} could be a linearly independent or linearly dependent set of vectors...

Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2...

Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that...
For the first question, could you please explain more specific, I can not understand the answer....

For the first question, could you please explain more specific, I can not understand the answer. For the second question, why the third choice with (1,1,0) is not correct? Can you explain it? Thx. Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, u3, u4). O True, since the span of {??, u2, u3, u4} is a subset of the span of {ul, u2, u3}. False....
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29...

1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...

1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for...

1- 2- 3- 1 (10 points) Show that {u1, U2, U3} is an orthogonal basis for R3. Then express x as a linear 3 4 combination of the u's. u -3 U2 = 0 ,u3 5 6 -2 2 -1 (10 points) Suppose a vector y is orthogonal to vectors u and v. Prove that y is orthogonal to the vector 4u - 3v. 10. (2 points each) True or False: ( ) Eigenvalues must be nonzero scalars. ( )...
Mark each statement as True or False and justify your answer. a) The columns of a...

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,...
Decide whether each statement is true or false and explain your reasoning. Give a counter-example...

Decide whether each statement is true or false and explain your reasoning. Give a counter-example for false statements. The matrices A and B are n x n. a. The equation Ax b must have at least one solution for all b e R". b. IfAx-0 has only the trivial solution, then A is row equivalent to the n x p, identity matrix. c. If A is invertible, then the columns of A-1 are linearly independent. d. If A is invertible,...

IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set o...

IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...