Use the definition of linear independence to determine whether the columns of the following matrix form a linearly independent or dependent set.
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Use the definition of linear independence to determine whether the columns of the following matrix form...
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...
Determine if the columns of the matrix form a linearly independent set. 1 2-3 1 2 5 - 4 -2 - 14 2 7 2 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of is A 0 B. The columns are linearly independent because the reduced row echelon form ofA 0 is
Testing for Linear Independence In Exercises 49-52, determine whether the set of vectors in M22 is linearly independent or linearly dependent. 32. A = (-; J.B-15 5C--817||
Determine if the columns of the matrix form a linearly independent set. 1 2 - 3 8 12 37 -6 38 - 1 -8 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of [ A o]is | The columns are linearly independent because the reduced row echelon form of [ A 0 ] is B.
help 6. (10 pts) a) Use the definition of linear dependence to show that following set of functions is linearly dependent: 1 + x2,3-22,5 1. Are these functions b) Evaluate the Wronskian of y1 = sin(2t), y2 = cos(2), and 3 linearly dependent or independent on R?
1. (5 pts) The reduced row echelon form of A is R. Determine whether the columns of A are linearly dependent or linearly independent, and clearly explain your answer. 1 1 1 0 0 0 0 0 0 0 0 1 8 0 9 2 9 4 5 9 9 9 9 4 7 6 9 8 9 = 1 R= 0 1 0 1 0 0 0 0 0 0
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,...
- What is the difference between linear independence and dependence - Is a matrix in gaussian form (reduced form) always linearly independent?
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...
1 Let A= 8 We want to determine if the columns of matrix A and are linearly independent. To do that we row reduce A To do this we add times the first row to the second. We conclude that A. The columns of A are linearly dependent. O B. The columns of A are linearly independent. O C. We cannot tell if the columns of A are linearly independent or not.